Model Predictive Control

Robots operating in physical environments make control decisions based on uncertain sensor measurements, which can lead to unsafe or suboptimal actions. Runtime monitors that check their behavior against safety specifications must represent this uncertainty soundly. Zonotopes are a widely used representation, but continuously incorporating new measurements grows their order unboundedly, so monitors must periodically apply an over-approximating reduction. The choice of the reduction method substantially affects the zonotope's precision, yet existing approaches typically utilize a fixed method throughout the run, even though the optimal choice depends on the current state. This paper presents a Predictive Zonotope Reduction (PZR) approach, which frames reducer selection as an optimal control problem and solves it using beam-search model predictive control. Policy distillation into a small neural policy further provides substantially higher execution speed than model predictive control while maintaining improved performance, enabling uncertainty-aware runtime monitoring on resource-constrained real-time systems. We implement our approach in the RLola runtime monitoring framework and evaluate it on a 5-degree-of-freedom robotic arm simulated in MuJoCo, with sensor uncertainty modeled according to ISO 5725. Experiments on a Raspberry Pi 5 show that dynamic reduction significantly lowers false-positive rates in monitoring compared with static reduction strategies.

Latent world models support efficient model predictive control from high-dimensional observations, yet optimizing a single learned latent objective can favor action sequences whose decoder-predicted terminal descriptor does not match the goal descriptor. We introduce Latent Energy Action Planning (LEAP), which treats the complete action horizon as a differentiable variable and optimizes it through a frozen LeWorldModel (LeWM). LEAP couples terminal latent goal matching with a terminal-window state energy. Low energy requires the predicted terminal latent to agree with the goal latent and the decoder-predicted terminal descriptor to agree with the goal descriptor. A frozen goal-conditioned proposal initializes the search, a quasi-Newton solver refines actions through the autoregressive rollout, and post-optimization projection enforces the admissible action range. Across four control domains using the officially released LeWM checkpoints, the complete LEAP planning system raises mean success from 77.5% for LeWM planned with the cross-entropy method (LeWM+CEM) to 94.8% under a matched protocol, a 17.3-percentage-point improvement, while retaining the frozen LeWM representation and predictor.

Intermittent state measurements pose fundamental challenges to model predictive control of constrained nonlinear systems because prediction uncertainty grows during feedback outages and measurement-triggered resets disrupt nominal state propagation, potentially compromising closed-loop stability and recursive feasibility. This paper develops a Koopman-based stochastic MPC framework with probabilistically truncated soft constraints. Specifically, a Lipschitz-constrained deep Koopman model provides a linear latent predictor, enabling computationally efficient online optimization. The intermittent measurement process is modeled as a two-mode discrete-time Markov chain, yielding a unified Markov jump error model for open-loop propagation and measurement-triggered resets. Under numerically verifiable sufficient conditions, the prediction error is shown to be mean-square ultimately bounded, and an explicit uniform second-moment bound is obtained. A distribution-free probabilistic error radius is then constructed for a prescribed confidence level and used to truncate dropout-dependent constraint tightening. An exact-penalty soft-constraint mechanism accommodates reset-induced jumps and prolonged dropouts. Under the stated terminal compatibility and bounded-disturbance conditions, recursive feasibility and mean-square ultimate boundedness of the closed-loop regulation error are established. Numerical simulations on a visual-servoing tracking task corroborate these theoretical results and demonstrate effective tracking under stochastic measurement unavailability.

This study proposes a novel Model Predictive Path Integral (MPPI)-based task-space control framework. The proposed framework explicitly solves rigid-body dynamics within a real-time MPC formulation and enforces safety constraints, enabling accurate motion and force control that yields compliant behaviors for safe and effective physical interaction of robotic manipulators in unstructured environments. By leveraging MPPI, the proposed framework efficiently handles nonlinear dynamics that are difficult to solve with conventional MPC approaches in real-time. Furthermore, we develop a torque-sampling-based control architecture that enables efficient exploitation of GPU-based parallelization, resulting in effective compliant and force-aware behaviors. As a result, the proposed framework achieves a solver update rate of over 166 Hz with a 0.18 s prediction horizon, and its performance is validated through real-world experiments on a 7-DoF manipulator.

We introduce a novel Divide and Conquer control design methodology leveraging differential games in single-agent, multi-objective dynamical systems. The proposed framework associates each control objective with a virtual input and establishes a non-cooperative, finite or infinite horizon differential game among representative players. Each player optimizes a distinct virtual cost function tailored to its specific goal, the full system state, and the other virtual inputs, while accounting for the remaining players' optimal policies. By establishing a Nash Equilibrium for this game, we synthesize a composite controller that achieves a stable balance across competing objectives, providing control engineers with an intuitive and modular framework for parameter re-tuning throughout the design cycle. We provide formal mathematical derivations for both continuous-time and discrete-time dynamical systems, targeting large-scale single-agent applications where complex, dynamically conflicting control objectives make global weighting intractable. To demonstrate the methodology, we developed an open-source Python package implementing a novel numerical algorithm for solving Coupled Algebraic Riccati Equations arising in infinite-horizon differential games. We evaluate the approach on two benchmark case studies: an inverted pendulum on a cart and a non-linear hierarchically controlled quadrotor. The resulting closed-loop performance is compared against the classical Linear Quadratic Regulator (LQR) across various transient and steady-state control metrics, demonstrating superior trajectory tracking and robust multi-objective regulation.

Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.

A long-standing open problem in robot manipulator control is whether global regulation can be achieved by classical PID control. This paper provides an answer to this question for classical PID controllers with triple parameters (k_p,k_i,k_d) in R^3. We find and prove that for one-degree-of-freedom manipulators, the classical PID control guarantees global stability and asymptotic regulation under standard structural assumptions, and further derive explicit quantitative design conditions for the PID gains. However, for multi-degree-of-freedom cases, we can construct a robot manipulator satisfying the same structural assumptions for which no choice of PID gains (k_p,k_i,k_d) can achieve global asymptotic regulation. These results provide a fundamental understanding of the abovementioned open problem, revealing both the fundamental capability and intrinsic limitation of the classical PID control for robot manipulator dynamics.

In Model Predictive Control (MPC), cost-function weights shape closed-loop behavior, yet changing conditions often make fixed parametrizations suboptimal and motivate context-dependent online adaptation. Learning such policies is difficult because behavior depends implicitly on numerical MPC solutions, producing nonlinear, potentially nonsmooth, long-horizon dependencies on policy parameters. This creates a bias-variance tradeoff: Reinforcement Learning (RL) optimizes realized closed-loop return from environment samples but is sample-inefficient, whereas Gradient-Based Policy Learning (GB-PL) uses low-variance solver gradients from differentiable MPC to optimize surrogate losses on predicted trajectories but can be biased under model mismatch. We propose Solver-Gradient Guided Reinforcement Learning (SG-RL), a solver-sensitivity augmentation for RL-based online MPC cost-weight adaptation. SG-RL keeps sampled closed-loop return as the objective and uses bounded solver-derived gradients as auxiliary guidance to improve stability and sample efficiency. We instantiate SG-RL in Proximal Policy Optimization (PPO) with four modular algorithms that inject solver-gradient guidance into actor-update scaling, policy loss, advantage estimation, and value-function learning. On two full-scale autonomous racing platforms with intentional model mismatch, SG-RL reaches PPO's best closed-loop return with up to 70.6% fewer samples, outperforms GB-PL baselines by at least 54% in closed-loop return, and generalizes zero-shot to unseen environments.

Combining learned policies with model predictive control can leverage learned task priors while retaining online adaptation to new objectives and constraints, but performance degrades when the policy is out of distribution. In policy-guided model predictive path integral (MPPI) control, a policy-centered warm-start approach centers the sampling distribution on the policy output. When the prior is mismatched, centering the sampling distribution on the policy output restricts exploration around an unsuitable solution and prevents recovery toward the task optimum. We propose Proximal Prior Injection (ProxPI), which retains nominal-centered MPPI sampling and incorporates the policy through a soft proximity cost. This matches the in-distribution performance of existing prior-injection schemes while enabling the optimizer to escape an inaccurate policy and recover vanilla MPPI-level performance. We theoretically show that re-centering on the prior discards the optimizer's correction at every update, whereas nominal-centered sampling retains it and converges to a solution set by both the task cost and the prior, and that this failure is not removed by a larger rollout budget. Simulations and real-robot experiments demonstrate robust performance under both in-distribution and out-of-distribution tasks.

Bridging model-based control and learned policies in long-horizon manipulation has harbored a silent disagreement: control executes specified objectives, learning amortizes that behavior into a reactive policy, yet existing protocols discard task semantics, leaving rewards hand-crafted and behavior drifting from what control verified.We introduce Semantically UNified (SUN) Programs, typed executables where geometric and contact relations are defined once and compiled into aligned Model Predictive Control (MPC) costs, satisfaction predicates, RL rewards, transition guards, and diagnostics. Our system, Kuafu, driven by large vision language systems, automatically synthesizes SUN Programs from language and scene semantics, screens feasibility via MPC, and retains semantics while training stage-conditioned policies. Across nine tasks, Kuafu achieves 82.03% macro-success, outperforming sparse-reward (35.67%) and Stage-BC (24.75%) baselines. At 8192-way scale, it generates 10.57x the successful trajectory time per hour of human teleoperation. With 500 trajectories per task, Kuafu data trains DP3 policies to 46.0% simulation success (vs. 22.4% for alternatives) and 34.7% on physical Franka and Kinova robots. These results establish that simulation-screened task semantics can effectively amortize control into robust policies, without demonstrations or manual dense rewards, unifying symbolic planning and data-driven execution.

This paper considers decentralized contingency MPC for multi-agent control under a state-only information pattern, with particular focus on limited sensing and plug-and-play operation. The objective is to retain recursive feasibility, safety, and Lyapunov-type convergence while reducing conservatism in local interaction handling. The framework relies on agent-wise fallback regions (safe sets) in which a feasible contingency maneuver to a safe equilibrium is always available. A novel safe-set update mechanism is introduced that supports less conservative decentralized interaction while preserving the underlying guarantees. This, in turn, enables memory-free local interaction and finite sensing ranges without requiring agents to reconstruct the exact neighbor geometry. The resulting scheme remains fully decentralized and preserves the shared-first-input contingency MPC structure. Theoretical guarantees and simulation results illustrate the effectiveness of the approach in dense multi-agent scenarios.

Physical learning lets a trainable material or network use its own physical response to carry error signals, reducing the need for a separately programmed backward computation. We ask what determines whether such a system follows conventional gradient descent or evolves along a genuinely different learning trajectory. Our canonical model is a directed layered transport network in which every node redistributes a fixed amount of flow, so learning preserves positivity and total mass. In this model, conservation constrains only the allowable learning directions. Within the matched response class studied here, adjoint matching gives the physical output response a symmetric form. Non-negative mode-wise feedback then produces a reciprocal closed-loop response and a reweighted gradient flow. Adding an antisymmetric boundary component makes the closed-loop response rotational: the learning path can turn while the error driving that update still decreases at that moment. Turning is not automatically beneficial. Its finite-step effect is set by local curvature, and its accumulated effect also depends on step selection and on the new states visited along the path. Numerical consistency checks reproduce the exact response structure, predict the sign of the local effect across new network families, and show how trajectory drift can negate a local advantage. These results separate the roles of conservation, reciprocity, and nonreciprocity in physical learning.

By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization in learning-enabled dynamical systems arising in data-driven optimization and feedback control approximation. Given two neighboring datasets, we specifically model sample replacement as an exogenous disturbance acting on a sensitivity system, while the incremental behavior of the data-dependent operator is encoded through an integral quadratic constraint. By relying on dissipativity arguments, we establish a matrix inequality-based certificate and a uniform stability bound that separates the one-sample sensitivity of the learned operator, and an algorithm-dependent dynamical gain. The latter can then be optimized, offering a tractable tool for certifying and comparing generalization capabilities of learning dynamics. We show that our results recover classical ones for gradient descent, apply naturally to momentum-based methods such as heavy-ball and Nesterov acceleration, and extend to data-driven control.

Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. This paper exploits an alternative geometry. For a fixed model-specific stability certificate admitting suitable physical lifts, the small-signal stability requirement becomes an affine positive semidefinite constraint in the lifted variables, thereby defining a convex certified safe region. Instead of approximating the nonlinear instability boundary itself, we optimize a sample-wise safe radius in the original uncertainty space and certify, in the lifted space, that the entire power-flow image of the corresponding uncertainty ball is contained in the convex stability region. To this end, a componentwise Perron certificate guarantees existence, uniqueness, and Jacobian regularity of the target AC power-flow branch throughout each ball. An adjoint elimination then provides an exact affine-quadratic representation of the stability-relevant quantities, while rigorous matrix remainder bounds convert their nonlinear variation into finite robust PSD constraints. The resulting radii are certified lower bounds on the distances from empirical samples to failure and can therefore be coupled directly to the distance-based reformulation of a Wasserstein distributionally robust chance constraint, without directly approximating the instability boundary. Numerical studies demonstrate the effectiveness of the proposed framework.

Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.

In the present work an efficient border control management procedure is proposed. Compared to operational queue management systems, whose operations are based on mostly static data, the proposed work takes into account dynamic traffic conditions, thus enabling optimal performance, even in cases of uncertainty. To this end, we are proposing a multi-modal Artificial Intelligence (AI) framework, tailored to th needs of border control systems, which enables real-time queue prediction, management, and resource optimization. The novel proposed approach integrates heterogeneous data sources and presents them through a unified representation by employing Long Short-Term Memory (LSTM) networks for queue forecasting. Furthermore, it leverages Model Predictive Control (MPC) and scheduling optimization to derive actionable control policies, which in turn can be presented to border control officers. The proposed work has been evaluated using synthetic data simulating realistic traffic. The evaluation results demonstrate that the proposed method reduces queue prediction error by up to 35% and average waiting time by 30%. Accordingly, the average throughput increases by nearly 20%, compared to ARIMA and rule-based methods. The abovementioned results show the effectiveness and efficiency of combining AI architectures with optimization techniques for proactive and adaptive border traffic management.

This paper presents a real-time control-constrained Differential Dynamic Programming (DDP) framework for underactuated legged robots. To address the limitation of classical DDP in handling control constraints, we propose an Accelerated Projected Gradient (APG)-based control-constrained DDP (ABC-DDP), which efficiently computes constrained solutions and identifies active sets without repeated Karush-Kuhn-Tucker (KKT) inversions. A virtual constraint is introduced to integrate control constraints within a feasibility-driven multiple-shooting framework, enabling stable optimization even from dynamically infeasible initializations. The proposed method supports real-time model predictive control (MPC) with short horizons under strong underactuation. Simulation results demonstrate static two-leg standing under external disturbances, along with diverse dynamic motions including slow catwalk, upright walking, and high-speed running within a unified MPC framework. To the best of our knowledge, this is the first demonstration of static two-leg standing of a quadruped robot achieved using real-time finite-horizon MPC.

Purcell's swimmer is a well-known planar model of a swimming microorganism, governed by low Reynolds number hydrodynamics, which is comprised of three rigid links connected by actuated rotary joints. This model has been analyzed as a robotic locomotion system governed by first-order nonlinear dynamics with a periodic input (gait) of the two joint angles. In this work, we present a robotic macro-scale realization of this three-link swimmer moving in a highly viscous fluid. We propose a simple variant of Purcell's theoretical model with non-slender links and a central rigid sphere which represents the added drag of the robot's central flotation block, and calibrate the model's parameters to fit experimental measurements. Next, we apply optimal control formulation based on Pontryagin's Maximum Principle (PMP) in order to find optimal gaits that maximize the displacement per cycle under bounds on the joint angles. Employing a differential geometric method that transforms the problem to area integral enclosed by the gait trajectory in the plane of joint angles, enables visual interpretation which explains topological changes in displacement-optimal gaits upon varying the bound on the joint angles. We then apply PMP formulation to the problem of maximizing Lighthill's energy efficiency in order to obtain a boundary value problem (BVP) whose solution gives efficiency-optimal gaits for Purcell's swimmer model, as well as its variant with a central sphere. Finally, we utilize numerical methods such as parameterizing the input gait as a truncated Fourier series, as well as GPOPS-II solver, to produce sufficient initial guess values for solving the BVPs and obtaining efficiency-optimal gaits.

Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the Block Decomposition Method, is piecewise constant, restricting the calculus to finite differences. We use $K^{\mathrm{CDM}}_{\mathrm{s}F}$, a certified, differentiable estimator, to bring the calculus into learning dynamics: grokking, where a complexity order parameter is known but has not been made to act. As a transient loss kick, the estimator becomes a controller that accelerates grokking in Levin's description-length--versus-time sense, within a data-dependent Occam boundary whose finite-size trend, $f_c\sim\ln p/p$, is consistent with a coupon-collector interpretation. Ablations show that a complexity gate matches a train-loss gate in rescuing failing seeds with $27\%$ less intervention; among the tested signals, only map complexity marks the transition's completion; the certified prior and the per-parameter $\nabla K$ attribution are both fungible (a uniform-prior sensor makes bit-identical gate decisions, and random supports match $\nabla K$-selected ones above a sparsity threshold); and direct field perturbation shows a nucleation-like response to the Occam field (no linear regime is resolved over the probed amplitudes, so these measurements do not justify a fluctuation--dissipation surrogate), with a finite-field response growing by orders of magnitude toward the phase-transition. These measurements account for the empirically tuned staircase: bang--bang pulses, stall-fired and released on yield, whose iteration plausibly builds the response it exploits. The kick transfers to sparse parity and to a transformer; a sustained weight-space loss fails. The algorithmic estimator's distinct contribution is timing (when to fire and when to release), not attribution.

In this paper, we formalize a joint communication-control strategy optimization (JCCO) problem in multi-agent linear systems with quadratic costs, under the common-information-based (CIB) framework from decentralized stochastic control. For computational tractability, we focus on such JCCO problems with partially nested (PN) information structures (ISs). In particular, with a baseline communication protocol that leads to a PN IS, we establish a series of conditions under which the partial nestedness is preserved under the (additional) communication strategies to be optimized, while violating them may cause nonlinearity of the optimal strategies in general, with open-loop communication strategies. We then develop a dynamic-programming-based approach to compute the optimal control strategies of JCCO with open-loop communication strategies, which yields a set of closed-form Riccati Equations. As a byproduct of independent interest, such an approach also offers a way to solve decentralized linear-quadratic control with PN ISs and output feedback, under the CIB framework. Finally, we extend such an approach to JCCOs with closed-loop communication strategies, yielding a more tractable dynamic program than an infinite-dimensional CIB-belief-based one.

We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target $$π(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d,$$ where $f$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g$ is convex and $G$-Lipschitz. Let $g_λ$ be the Moreau envelope of $g$, $π_λ$ the corresponding smoothed target, and $a_λ=\operatorname{tr}H_λ$, where $H_λ$ is the a.e./weak Hessian of $g_λ$. We show that the leading MYULA discretization error is controlled by the reference active trace $B_{\mathrm{ref}}$, the average of $a_λ$ along the heat substep of one MYULA update started from $π_λ$, rather than by the global curvature bound $d/λ$. If $M_λ$ is an a.e. upper bound for $a_λ$, then, up to logarithmic factors, $$N \lesssim \frac{1}{m} \left[ L_f + \frac{ τ_f+G^2+B_{\mathrm{ref}} }{ \varepsilon_{\mathrm{alg}}^2 } + \frac{M_λ}{\varepsilon_{\mathrm{alg}}} \right], \qquad τ_f:= \sup_x\operatorname{tr}\nabla^2 f(x),$$ iterations suffice to ensure $\sqrt m\,W_2(μ_N,π_λ)\leq\varepsilon_{\mathrm{alg}}$, where $μ_N$ is the law of the $N$-th iterate and $W_2$ is the quadratic Wasserstein distance. We also prove the Moreau-bias bound $$\sqrt m\,W_2(π_λ,π) \leq \frac{G^2λ}{4}.$$ Thus, choosing $λ\asymp\varepsilon/G^2$ gives an end-to-end guarantee for $π$. The universal estimate $B_{\mathrm{ref}}\leq d/λ$ yields $\widetilde O(\varepsilon^{-3})$ accuracy dependence. For the structured piecewise-linear, lasso-type, group, and total-variation penalties considered here, curvature--tube estimates make $B_{\mathrm{ref}}$ independent of $λ$, yielding $\widetilde O(\varepsilon^{-2})$ for the same classical MYULA kernel.

Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.

Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an $\textbf{A}$DMM-$\textbf{I}$nspired $\textbf{M}$omentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem determines the acceleration form. Building on AIM, we propose $\textbf{R}$elativistic $\textbf{A}$daptive gradient $\textbf{D}$escent with $\textbf{A}$ccelerated $\textbf{R}$esidual (RADAR), which combines relativistic adaptive geometry, decoupled residual correction, and second-order momentum filtering to improve the update direction and momentum estimation. We establish stochastic convergence through a variance-perturbed Lyapunov drift analysis. Experiments on supervised vision learning, language modeling, and reinforcement learning show that RADAR achieves consistent improvements over strong adaptive optimizer baselines.

Distribution steering seeks feedback laws that drive the state law of a dynamical system between prescribed initial and terminal distributions. Optimal transport provides a natural geometric approach, but its implementation generally requires a transport map or coupling in the full state space. Sliced optimal transport avoids this full-dimensional construction through one-dimensional projections. Yet, the resulting projected maps specify only directional displacements and do not by themselves prescribe a realizable feedback law. To this end, we develop a finite-horizon control framework based on sliced optimal transport. At each sampling instant, a projected optimal transport map defines a directional terminal condition, whose minimum-energy realization yields a randomized single-direction controller. Averaging over projection directions gives a deterministic sliced feedback. For the single-integrator dynamics, the averaged feedback makes the sliced Wasserstein distance to the target non-increasing. For Gaussian endpoint laws, it is affine, preserves Gaussianity, and steers the mean and covariance to their prescribed terminal values. We further identify a law-dependent gain that yields linear decay of the sliced Wasserstein distance together with an explicit characterization of the control energy. We also prove that the randomized controller converges to the averaged sliced flow as the sampling period vanishes. Finally, we extend the construction to linear dynamical systems. Reachability-normalized coordinates allow instantaneous realization of the sliced velocity for uniformly fully actuated systems, while local controllability Gramians provide exact finite-step realization for general controllable systems. Numerical examples illustrate the resulting distributional flows.

A vehicle seeking a hidden target through a range-bearing relay of unknown position and yaw must decide, online, whether its own motion has already made the relay calibration trustworthy, and what to do when it has not. Two distinct vehicle-relative observations are known to remove the calibration gauge and make the target's relay-local packet globally actionable (arXiv:2608.09464), but that statement is static: it classifies a stored window only after the fact. This paper supplies the closed-loop layer: we show that the trajectory-spread margin $S_v$ that governs identifiability is simultaneously a finite-noise seed-accuracy bound, a local-vector variance decomposition, and a circle-geometry excitation budget, and we use it to supervise an excitation-reset controller. An excitation-supervised algorithm retriggers exploratory motion whenever the spread certificate is insufficient, projecting the target-seeking input away from the excitation's push, and otherwise proceeds to unrestricted target seeking. Under explicit sampling assumptions the supervision rule provably acquires any required excitation in finite time; in the noiseless local regime with positive excitation decay, estimator convergence yields target-seeking convergence after certification; and the threshold is selected from a desired calibration-accuracy level rather than chosen heuristically. Closed-loop simulation, paired Monte Carlo comparisons, a spread-threshold ablation, and a ROS 2/Gazebo software-in-the-loop experiment with sensing delay validate the approach. A decay-rate sweep shows that supervision matters when a fixed schedule's decay outruns the unknown time-to-adequate-excitation: over 100 paired trials the fixed baseline's yaw RMSE rises from 0.010 to 0.065 rad and success falls to 56%, while target-tracking error remains insensitive; supervision keeps yaw RMSE between 0.0095 and 0.0191 rad with 100% success.

Integrating locomotion and manipulation is essential for robot autonomy, but scaling standard Reinforcement Learning (RL) to complex tasks is severely bottlenecked by the slow, manual process of dense reward shaping. To bypass this limitation, we leverage Sample-based Model Predictive Control (SMPC) entirely in simulation as an automated, rapidly tunable expert to generate massive offline datasets. Because this data solves the fundamental exploration problem, we can train an off-policy RL agent using purely sparse task rewards, drastically reducing the time required to learn new skills and eliminating the need for manual tuning. Integrating this high-level agent with a low-level dynamic stability controller yields more optimal behaviors that strictly align with true task objectives, ultimately allowing the learned policies to surpass the original optimal control teacher. We validate the robustness of this sim-to-real framework by successfully deploying complex loco-manipulation skills across different morphologies, including an arm-equipped Spot quadruped and a G1 humanoid.

The computability of real numbers and functions using Turing Machines has been a central area of theoretical computer science since the mid-20th century. In the late 20th century, it was shown that chemical reactions can serve as a basis for computation using the Chemical Reaction Network (CRN) model. Recent advances in computing real numbers using Deterministic Chemical Reaction Networks (DCRNs) have identified numerous classes of DCRN-computable real numbers. In parallel, the works of R. Landauer and C. H. Bennett, spanning the 1960s to the early 2000s, showed that reversible computing offers significant advantages over irreversible methods, particularly in energy efficiency, motivating extensive research on reversible computation. In this work, we investigate the computability of real numbers using Reversible Chemical Reaction Networks (RevCRNs). The paper has two primary contributions: (1) establishing relationships among CRN-computable real number classes including Lyapunov CRN ($\mathbb{R}_{LCRN}$), Real-Time CRN ($\mathbb{R}_{RTCRN}$), rational numbers ($\mathbb{Q}$), and RevCRNs ($\mathbb{R}_{RevCRN}$), with key results: (i) $\mathbb{Q}$ is a strict subset of $\mathbb{R}_{RevCRN}$; (ii) the set of positive algebraic numbers ($ALG$), $\mathbb{R}_{LCRN}$, and real numbers computable by 1-species RevCRN ($\mathbb{R}_{RevCRN}^{1s}$) are equal; (iii) $\mathbb{R}_{RTCRN}$ and $\mathbb{R}_{RevCRN}$ exhibit non-empty overlap; and (iv) the set of real numbers computable by detailed-balanced RevCRNs ($\mathbb{R}^{DetBal}_{RevCRN}$) is a subset of $ALG$; and (2) exploring the existence of a hierarchy within $\mathbb{R}_{RevCRN}$. Finally, we leave open the exact relationship between $\mathbb{R}_{RevCRN}$ and $\mathbb{R}_{RTCRN}$ while conjecturing a general hierarchy of RevCRN-computable reals.

In this work, we study the information bottleneck under perfect privacy, with particular emphasis on the active-rate regime, where the representation-rate constraint is binding and directly limits the achievable utility. The goal is to construct a representation that preserves utility-relevant information while remaining statistically independent of a sensitive variable. This exact independence requirement introduces an additional constraint beyond the classical rate-relevance tradeoff and must be explicitly incorporated into the optimization. To this end, we develop an alternating direction method of multipliers (ADMM)-based method tailored to the resulting problem structure. Under suitable regularity conditions, we establish global convergence of the generated sequence, characterize its convergence rate through the Kurdyka-Lojasiewicz exponent, and extend the analysis to inexact block updates.

A growing class of methods probes a language model by feeding it its own output: self-consistency, iterated refinement, agentic loops. We ask what such a probe measures, in a construction chosen to make the question sharp: a ring of token cells resampled in place by the model's own windowed conditional p_r(x_i | x_{i+-r}). The substrate is Glauber dynamics on token sequences and is not new; what we change is the coupling. Advancing two rings that differ in one token under common random numbers makes undamaged copies diverge by exactly zero, so damage spreading becomes measurable where a maximal coupling gives mixing times instead. The answer is that it measures two different things at once, in readings that look alike. Some quantities are fixed by the construction: the damage light cone is kinematic, and the radius scaling of the token-space Lyapunov exponent lambda_ca(r) is model-invariant across 19 models and two scale ladders spanning 70x. Others genuinely track the model: lambda_ca crosses zero at a reproducible point in training, and the attractor share ranks models consistently however the lattice is built. Left undistinguished, the first kind is readily mistaken for the second -- we did so ourselves for four months, and report a phase transition we measured to three decimal places that belongs to the probe rather than to any language model. We give the test that separates them: hold the construction fixed and vary the model, or hold the model fixed and vary the construction, and see which readings move. We validate the instrument by reproduction first, recovering a Domany-Kinzel damage field bit-exactly against an independent prediction, and we report the estimator failures that this discipline caught -- four retracted verdicts, each on a quantity that looked like a measurement. The methodology ships as a package.

Runtime hazard monitors for autonomous naviga- tion are conventionally built from geometric quantities: predicted clearance, time to collision, and required deceleration. A model-predictive controller that enforces safety through explicit con- straints computes, as a by-product of every control step, a second information channel that such monitors ignore: the Karush-Kuhn-Tucker multipliers of its constrained optimization, which measure the marginal control effort spent to maintain safety against each obstacle. This paper evaluates whether a horizon-weighted sum of those multipliers, a dual stress signal, provides a hazard monitor complementary to the geometric warnings the same state already supports. We compare it against a battery of fifteen geometric detectors tuned to a matched false-alarm budget, on preregistered held-out crossing scenarios driven through a physics simulator. The stress alarm actionably flags 4.7 times as many collisions missed by the entire geometric battery as the geometric battery flags in return (85 versus 18); combined, the two channels warn of three quarters of the collisions for which braking remained feasible, against under half for the geometric battery alone.

Linear Quadratic Stochastic Optimal Control (LQ-SOC) establishes a fundamental framework for steering noisy dynamical systems and has recently gained renewed interest in the machine learning community. However, current state-of-the-art policy-based methods suffer from prohibitive computational costs and instability due to their heavy reliance on full-trajectory simulation. To overcome these limitations, we propose a paradigm shift toward a value-based approach by revisiting Path Integral Control (PIC). Although standard PIC suffers from the same high-variance bottleneck as policy-based methods, we discover that by truncating and marginalizing the original path integral formulation, we can derive a temporal recursive form of the value function. Building upon this theoretical foundation, we propose the Path Integral Value Matching (PI-VM) algorithm. Specifically, we employ temporal-difference learning to approximate the recursive value dynamics, and further integrate the Girsanov theorem with experience replay to enable off-policy training. We benchmark PI-VM against SOTA policy-based methods across various SOC benchmarks and sampling tasks. Empirical results demonstrate that PI-VM matches SOTA precision with an order-of-magnitude efficiency gain in low-dimensional settings, while effectively mitigating mode collapse in high-dimensional scenarios. Consequently, PI-VM offers a scalable solution for solving complex SOC problems.

Contact-based industrial inspection requires aerial platforms to maintain stable interaction while rejecting disturbances. Underactuated aerial manipulators present control challenges due to the dynamic coupling between vehicle attitude and force generation. This paper proposes a robust control framework for an underactuated hexarotor equipped with a 1-DoF manipulator to perform sustained contact inspection. The architecture integrates integral-augmented Sliding Mode Control (SMC) for trajectory tracking with an admittance control law for force regulation. The contact force is mapped to a feedforward attitude term, while the 1-DoF arm actively compensates for the tilt to maintain surface alignment. Software-in-the-loop simulations demonstrate that the SMC-based approach achieves superior tracking and coupling rejection compared to traditional PID. Furthermore, the interaction strategy achieved precise force regulation with an RMSE of 0.12N and was able to stably exert up to 20N force, confirming the system's efficacy for stable, reliable contact-based inspection.

Autonomous mid-air docking of multi-rotor vehicles under disturbance-driven target motion poses a constrained non-linear trajectory optimization challenge. This work formulates the docking task as a finite-horizon optimal control problem based on a reduced-order nonlinear model augmented with disturbance states. The resulting problem is solved using sequential convex programming within a receding-horizon framework to generate dynamically feasible docking trajectories. State estimation with noisy measurements is incorporated to enable robust relative motion prediction, while trajectory execution is validated in a high-fidelity rigid-body MuJoCo simulation environment. The proposed framework is evaluated for stationary and constant-velocity target motions, demonstrating reliable convergence to the docking interface while satisfying geometric capture constraints. Quantitatively, the method maintains negligible docking-cone violations and terminal state errors within prescribed tolerances, and achieves consistent, safe docking performance for cone half-angles as low as 10 degrees. Robust operation is observed for wind disturbance levels up to a standard deviation of 0.5, while preserving bounded approach velocities and stable control effort. These results demonstrate the effectiveness of the SCP-based trajectory optimization framework for disturbance-robust aerial docking under estimation uncertainty.

Volatility control converts risk estimates into portfolio exposure, yet existing approaches often rely on a fixed volatility estimator or a pre-defined control rule that may not adapt to changing market conditions. We propose VolRouter, a modular framework that formulates volatility control as state-conditioned routing over estimator-controller pairs. VolRouter first summarizes market conditions into a control-relevant state profile and then performs routing through three stages: state inference, switch review, and pair selection. The Router can be implemented using rule-based, learnable, or LLM-based decision modules, while portfolio actions remain generated by predefined control policies. We evaluate VolRouter across S&P 500, Multi-Asset, Bitcoin, and USDT volatility-control settings. VolRouter achieves the highest Sharpe ratio in three of four settings. On S&P 500, it improves Sharpe from 0.952 for RV + Naive Scaling to 1.222 while reducing maximum drawdown from 15.10% to 12.58% and daily CVaR from 1.76% to 1.32%. On Multi-Asset, it improves Sharpe from 1.498 to 1.540 and reduces CVaR from 1.56% to 1.18%. Bitcoin shows similar improvements in risk-adjusted performance, while USDT provides a boundary case where simpler state-aware selectors remain competitive. Ablation and sensitivity analyses show that the improvement comes from relative policy evaluation and selective persistent switching rather than simply expanding the policy library. These results suggest that volatility control can be viewed as a policy-selection problem when risk management requirements vary across market states.

Direct teleoperation of vehicles faces critical technical bottlenecks: communication latency and the operator's inability to physically perceive unmodeled environmental disturbances (e.g., aerodynamic drag, bank angles) coupled with highly nonlinear tire-road dynamics. To address these challenges, we propose a tailored unilateral teleoperation framework. The system integrates the Wave Variable (WV) approach to passively guarantee stability under stochastic delays, and an adaptive Radial Basis Function Network (RBFN) to actively compensate for vehicle-specific uncertainties. Unlike existing WV-neural network architectures designed for bilateral robotic arms, our framework features decoupled adaptive laws specifically designed for vehicle longitudinal and lateral dynamics. Furthermore, compared to model-heavy predictive controllers, the model-free RBFN offers rapid online adaptation without heavy computational overhead. Building upon our preliminary theoretical formulation, this brief paper presents comprehensive comparative analyses and real-world hardware validations. Simulation benchmarks against PID, LQR, MPC, and NMPC demonstrate that the RBFN achieves superior robustness against unmodeled disturbances while requiring orders of magnitude less execution time than MPC and NMPC, making it ideal for resource-constrained vehicle edge computing. Finally, hardware-in-the-loop experiments using a 1/10th scale vehicle over a 4G network validate the system's practical feasibility, safety, and robust trajectory tracking under physical road uncertainties.

Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.

Competitive artificial-life systems can rank trained controllers differently under training and ecological evaluation. We present Neuroevolution Arena, a GPU-accelerated spatial ecology of independently parameterized neural-network cells, and an audit-tracked nested evaluation protocol. Three implementation-specific update-and-inheritance regimes (EvoEvo, EvoRL, and RLRL) are crossed with two neural architectures for 50,000 generations in three independent training runs per condition. One saved elite-controller artifact from each of the 18 runs enters an aligned-run frozen-evaluation design comprising 198 computational jobs. Pairwise effects average three seed-defined ecological contexts (two cooperation-permitting and one attack-permitting) within each aligned training-run block; the independent level remains n = 3 runs per condition. RL-enabled regimes attain higher recorded training fitness than EvoEvo, whereas pairwise outcomes show architecture-conditioned majority patterns and substantial artifact dependence. Six-way winners vary across artifacts and contexts, and the prespecified survival endpoint has a complete floor. We contribute a nested protocol that separates training-run artifacts from evaluation contexts and exposes, rather than conceals, their different sources of variation.

Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks. We evaluate this prior under a controlled protocol in which an HNN and a parameter-matched feedforward baseline are trained on the same RK4-generated trajectories, use the same central-difference derivative targets and optimization settings, and are integrated at inference with the same RK4 scheme. Results are reported over five independent training seeds. On the nonlinear pendulum, the HNN reduces mean energy drift by 42-fold and mean trajectory MSE by 15.8-fold at T = 100, approximately 16 pendulum periods. Its energy drift also remains bounded and exhibits substantially lower seed-to-seed variability than the standard-network baseline. An energy-stratified analysis shows that the difference becomes more pronounced as trajectories explore more nonlinear regions of phase space. As an additional diagnostic, we examine an explicit Störmer--Verlet-style rollout of the learned HNN. Because the learned Hamiltonian is not constrained to the separable form H(q,p) = T(p) + V(q), the standard symplecticity guarantee of velocity Verlet does not directly apply. We further apply the same matched-integrator protocol to the three-dimensional Kepler two-body problem. The HNN again exhibits lower trajectory, energy, and angular-momentum drift than the parameter-matched baseline. These experiments provide a controlled study of how Hamiltonian parameterization affects long-horizon prediction and physical consistency across two conservative dynamical systems.

Recent advances in learning-based control have enabled impressive achievements in solving complex control problems in various domains. However, since learning-based control may not be able to realize safety-guaranties, it is of great importance to enhance safety and robustness while maintaining good performances. Take vehicle motion & dynamics control as an example, in order to overcome the pain points of traditional methods such as heavy parameter calibration effort and learning-based control to bring better performance and efficiency in stability & agility over prior work for state-based vehicle control tasks, in this work, our method aims to develop a curriculum learning controller enhanced with physics-based predictive safety filter. The validation is conducted with the Python-CarSim platform, demonstrating better improvements and scalability under various maneuvers.

Strictures caused by esophageal cancer can narrow down the esophageal lumen, leading to dysphagia. Palliation of dysphagia has driven the development of a Robotic Soft Esophagus (RoSE), which provides a novel in vitro platform for esophageal stent testing and food viscosity studies. In RoSE, peristaltic wave generation and control were done in an open-loop manner since the conduit lacked visibility and embedded sensing capability. Hence, in this work, RoSE version 2.0 (RoSEv2.0) is designed with embedded Time Of Flight (TOF) and pressure sensors to measure conduit displacement and air pressure, respectively, for modeling and control. Model Predictive Control (MPC) of RoSEv2.0 is implemented to govern the peristalsis and air pressure profile autonomously. The implemented MPC used Sparse Identification Nonlinear Dynamics with Control (SINDYC) models to estimate the future states of ROSEv2.0. The dynamic models are discovered from the TOF and pressure sensor data. Peristalsis waves of speed 20 mm/s, wavelength 75 mm, and amplitudes 5, 7.5, and 10 mm were successfully generated by the MPC. Additionally, RoSEv2.0 with the MPC was employed to perform stent migration testing with various food bolus consistencies. The major contribution claimed in this paper is the application of SINDYC-based MPC to solve the closed-loop control problem of RoSE for achieving desired peristaltic waves.

Multi robot teams performing cooperative transportation face a fundamental challenge: maintaining stable control while keeping communications efficient. This paper investigates how adaptive sampling time adjustment informed by measured network delay and strategic leader rotation can distribute wireless load fairly across the team. We use physics based simulation in MuJoCo with realistic wireless modeling, including time division multiple access, medium access control, jitter, queueing, and packet loss, to evaluate three control approaches: fixed sampling with static leadership, dynamic sampling with static leadership, and dynamic sampling with rotating leadership. Our results reveal an important trade off: dynamic sampling effectively reduces communications overhead without compromising control performance, while rotating the leader role meaningfully improves how fairly airtime is distributed all with negligible impact on the team carrying ability. to the best of our knowledge, being among the first to jointly examine dynamic sampling, rotating leadership, and wireless protocol interactions in physicsrealistic multi robot cooperation, this work provides practical guidance for deploying coordinated robotic teams in real world settings where communications resources are limited.

Multistage stochastic model predictive control (MPC) handles uncertainty by optimizing over a scenario tree, a finite branching approximation of future outcomes constructed from sampled forecasts. To build such a tree, conventional methods focus on matching the underlying probability distribution---e.g., via Wasserstein-based scenario reduction---but improved distributional accuracy does not necessarily yield better control performance. We propose a control-oriented approach that learns scenario tree construction directly from its impact on downstream decisions. Fixing the tree topology, we formulate tree construction as a sequential assignment of sampled scenarios to leaves. This assignment is parameterized by an attention-based policy over the scenario set and trained using reinforcement learning, with closed-loop control profit as the objective. Training is stabilized by an asymmetric critic that leverages realized future trajectories. We evaluate the method on a risk-averse battery arbitrage problem. Across a range of forecast set sizes, the learned construction consistently achieves the highest profit, outperforming classical forward and backward reduction methods and certainty-equivalent (single-trajectory forecast) control. The learned policy also exhibits greater robustness on challenging instances, consistently demonstrating better tail-risk characteristics. Analysis of the resulting trees indicates that our method constructs compact, selectively branching structures that capture high-impact events while keeping most trajectories nearly deterministic. These findings highlight that the value of a scenario tree depends critically on the decisions it supports, and provide an effective framework to train scenario tree constructors merely based on the closed-loop control optimization signal.

The 4th "AI Olympics with RealAIGym" competition, to be held at IJCAI-ECAI 2026 in Bremen, challenges participants to develop a global control policy for swinging up and stabilizing an underactuated two-link system in its upright position. In contrast to previous editions, participants develop and evaluate their control strategies directly on remotely accessible CloudPendulum hardware, with limited interaction time and without prior knowledge of the system's model parameters. This paper presents an optimal-control-based approach employing real-time nonlinear model predictive control implemented using sequential quadratic programming. The results demonstrate that the proposed SQP-based MPC controller achieves reliable swing-up and stabilization performance, while maintaining robustness against disturbances.

With the continuous improvement of computational capabilities, end-to-end reinforcement learning has been rapidly developed for remotely operated vehicles control. Nevertheless, existing end-to-end reinforcement-learningbased methods still face challenges in achieving optimal control under oceancurrent disturbances. In particular, there remains a lack of a unified control framework that can simultaneously achieve low steady-state tracking error, rapid transient response, energy-efficient operation, and smooth controlforce outputs under disturbances. To address the issue, this paper proposes the thrust smoothness rapid current adaptation proximal policy optimization (TSRCA-PPO) method which learns a near-optimal strategy by a twostage distillation learning framework. The core innovations of this work lie in the reward-function design and the privileged multi-encoder architecture. Ablation studies validate the effectiveness of each module. Simulation results demonstrate that the proposed TSRCA-PPO method consistently outperforms the conventional cascaded P-PID controller across all evaluation metrics. Specifically, TSRCA-PPO reduces the steady-state position error, steady-state attitude error, settling time, energy index, and thrustsmoothness index to 42.7%, 76.5%, 10.6%, 93.5%, and 15.9% of the corresponding P-PID values, respectively.

We study constrained statistical learning over infinite-dimensional hypothesis classes in the fully nonconvex setting, and establish universal PACC learnability of the solutions of dual algorithms: Probably Approximately Correct on Constraints, guaranteeing optimality and constraint satisfaction at once. This strengthens near-PACC results, whose feasibility residual no amount of data can remove. Optimality is caught between generalization, governed by Rademacher complexity and favoring small classes, and strong Lagrangian duality, which rests on Lyapunov convexity for vector measures and needs decomposability, a demand pulling the other way. We reconcile the two by posing the population problem over a universal RKHS $\mathcal{H}_K$, dense in a decomposable envelope, and learning over norm balls of growing radius. This yields the Tikhonov complexity $\mathfrak{T}^{\varepsilon}_{n}$, the least RKHS norm reaching an $\varepsilon$-optimal Lagrangian level set; we prove it finite, obtain exact learnability of the optimal value, and make the sample threshold explicit and polynomial in $1/\varepsilon$ under a source condition. Feasibility is harder: absent convexity the Lagrangian may not attain its infimum, and dual information pins down only an averaged constraint-risk vector, not the risks of any returned predictor. We introduce the closure-realization gap $\varepsilon^\star_\infty$, an index of how well $\mathcal{H}_K$ retrieves feasible solutions from dualization; it is a property of the problem, not of a modeling choice. Learnability is exact when $\varepsilon^\star_\infty=0$, in particular under dual differentiability, and near-PACC with residual exactly $\varepsilon^\star_\infty$ otherwise. Finally, no distribution-free threshold exists already in the unconstrained specialization, so universality is the canonical frame for dual algorithms over large hypothesis classes.

Safe robot navigation in crowded spaces requires planning that accounts for where people will be, not only where they are now. Model Predictive Path Integral (MPPI) control is an effective sampling-based planner, but many implementations encode humans as static point obstacles at their current positions, underestimating risk in dynamic scenes. We propose Predictive Gaussian Interaction Fields (PGIF), a spatiotemporal cost formulation that propagates pedestrian predictions forward over the full planning horizon and encodes them as anisotropic Gaussian repulsive fields aligned with each pedestrian's direction of motion. The forward spread of each field grows with the pedestrian's speed, creating a motion cone danger zone that penalises robot trajectories entering the pedestrian's path of travel more strongly than those approaching from behind. The formulation is closed-form and fully parallelisable across rollouts, adding no measurable computational overhead. Evaluated over 300 randomised crowd scenarios at three density levels, PGIF-MPPI achieves a 0% collision rate at every density level, compared with up to 82% for vanilla MPPI, while maintaining real-time planning performance.

This paper presents a scalable lateral control framework for robust path tracking of single-body and articulated autonomous vehicles at high speeds. A clothoid-based controller is extended with three key adaptations: 1) an integrated tangential check and Frechet distance method for optimized lookahead and oscillation mitigation; 2) real-time trajectory segment classification for dynamic adjustment of the lookahead search range; and 3) a dual-adaptive, rate-controlled lookahead mechanism responsive to cross-track error and upcoming path geometry. To support different vehicle configurations, the framework also incorporates flexible tracking point selection and curvature-to-steering lookup tables, enabling control of points such as the tractor rear axle, hitch point, or trailer-related locations without changing the core control architecture. The controller is evaluated using high-fidelity TruckSim and Simulink simulations for both standalone and articulated vehicles across dual lane changes and winding-road scenarios. Results demonstrate stable high-speed path tracking, reduced oscillations, effective lookahead adaptation, low cross-track errors, and acceptable lateral acceleration across different vehicle configurations. The results support the use of a unified lateral control architecture that can scale from single-body to articulated autonomous vehicles.

Robotic table tennis serves require high ball velocity and spin while respecting the robot's kinodynamic limits. Unlike rally strokes, a valid serve must also bounce on the server's side and clear the net, yielding a hybrid system with nonlinear flight and impact dynamics. We formulate spin-controlled serve generation as an event-time \ac{OCP} that optimizes the racket impact velocity and orientation together with the bounce, net-crossing, and landing times, enabling direct enforcement at phase boundaries of table-bounce and net-clearance constraints. The racket velocity and orientation are then converted into a complete kinodynamically feasible motion through a second \ac{OCP} enforcing joint-position, velocity, and torque limits. We evaluate the method numerically and on a KUKA Agilus robot. Compared with a fixed-step formulation with root localization, the proposed event-time formulation reduces the median solve time by a factor of 4.1 while maintaining comparable landing accuracy, spin accuracy, and serve validity. Real-robot experiments demonstrate controlled placement and topspin, backspin, and sidespin serves, with a mean landing error of $13.1 \pm 7.3$cm and spin rates up to 30rps. These results show that event-time optimal control efficiently generates physically valid, kinodynamically feasible serves while accounting for nonlinear aerodynamic and impact effects.

This paper presents a parameter-dependent linear matrix inequality (LMI) framework for trajectory tracking of nonholonomic mobile robots subject to severe multiplicative wheel slip on variable-terrain surfaces. The sampled convex formulation, augmented with grid-to-continuum residual certification, simultaneously establishes semi-global differential input-to-state stability, a prescribed exponential decay rate, regional pole placement, and a gain-bounded feedback proxy for actuator-limited operation. A central contribution is an explicit upper bound on the additive disturbance induced by bounded multiplicative slip in the Kanayama error coordinates, bridging the physical slip mechanism and the convex synthesis paradigm. The auxiliary gain matrix and inverse storage metric are parameterized affinely in the reference velocities, while the storage metric inherits nonlinear dependence through pointwise matrix inversion. Stability is established via a cascade analysis combining variational contraction, forward invariance, slip-induced disturbance bounds, and dissipation-based trajectory reconstruction. Numerical validation compares three controllers across six reference trajectories, six disturbance classes, and a 60-second variable-terrain test featuring six severe slip patches with bidirectional slip ratios reaching +/-50%, replicated on two geometries. Supplementary studies address Gaussian sensor noise, compound stress-testing, and embedded-platform computational feasibility. Across 100 Monte-Carlo runs the proposed controller achieves complete trajectory containment within the certified envelope. On the variable-terrain scenario, peak tracking error is reduced by 12% against the fixed-gain LMI baseline and 49% against the manual baseline, with the constant-gain baseline infeasible at the prescribed decay rate.

Safe and efficient robot navigation in crowds requires anticipating pedestrian motion despite uncertain and potentially shifting prediction errors. Existing reactive methods can produce oscillatory behavior, while predictive planners often treat forecasts as exact or rely on restrictive error models. Incorporating conservative uncertainty sets as hard constraints can also render model predictive control (MPC) infeasible. We propose \textit{CoCoNav}, a crowd-navigation framework that combines online conformal calibration with runtime-certified planning. A horizon-specific conformal proportional--integral controller adapts trajectory-error bounds to regulate long-run empirical coverage, enabling the framework to respond to changing prediction errors. A \textit{relax-then-verify} planner preserves solver feasibility by generating nominal trajectories with soft-constrained MPC and separately certifying them, together with contingency maneuvers, against the calibrated bounds before execution. Simulations and quadruped experiments show that CoCoNav achieves a favorable balance among collision avoidance, task success, and navigation efficiency relative to the evaluated baselines.

Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space. We study entropy-regularized discounted linear-quadratic (LQ) control. A Bellman verification argument shows that the unrestricted problem has a linear-Gaussian optimal policy, and the discounted-occupancy-weighted statewise Wasserstein gradient is tangent to this policy class. WPG therefore reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance. We prove that this ODE is globally well posed and converges exponentially from every admissible initialization. For each fixed LQ problem, the exponent has a positive limit as the entropy temperature tends to zero and contains no perturbative factor of the form $\exp(-c/τ)$, while retaining the usual dependence on the conditioning of the control problem.

Modern manufacturing imposes six coupled demands on adaptive control: local decisions with global consequences, partial observability, nonstationarity, reflex speed response with long horizon effects, delayed and diffuse outcomes, and dynamics that resist explicit modeling. Cooperative multiagent reinforcement learning (MARL), posed as a Dec-POMDP under centralized training with decentralized execution, is a particularly natural formalism for these demands. This paper adopts a MARL centered scope and asks where large language models (LLMs) should augment, interface with, train, or, in the strongest competitive case, replace that coordination core. A taxonomy organizes the literature through four LLM attachment points: policy, reward design, communication between agents, and hierarchical planning. A conditional capability profile separates native mechanism, reported performance, formal guarantee, and engineering maturity, and a deployment readiness analysis identifies the evidence behind each role. These stages yield the principal contribution: a three layer MARL centered reference architecture, grounded in evidence, for semantic reasoning, adaptive cooperative control, and independently assured execution. The LLM-Augmented Dec-POMDP is a descriptive comparative notation for that architecture, recording four attachment choices without introducing a new decision process class or algorithm. Under the reviewed evidence, conventional MARL is better suited to frequent, structured, decentralized coordination after task specific training, whereas LLM components are promising for semantic interpretation, reward drafting, human interaction, and slower supervisory planning. Current LLM only manufacturing controllers do not yet establish equivalence for strict real time, decentralized, safety critical control; this conclusion is bounded by the available evidence and does not assert impossibility.

Although remarkable capabilities have been demonstrated by Large Language Models (LLMs) across scientific domains, feedback controller design remains underexplored. Existing benchmarks focus mainly on linear single-Degree-of-Freedom (DoF) systems and large API-hosted models, leaving performance on complex controller-design tasks and feasibility for edge deployment unclear. To address these limitations, we introduce the Complex Dynamics-to-Control Benchmark for Large Language Models (CoDyControlBench), comprising 132 system configurations across five evaluation dimensions: number of DoF, system type, coupling level, damping regime, and controller type. Six state-of-the-art LLMs were evaluated over three independent runs, including three commercial models (GPT, Gemini, and Claude) and three open-source models (GLM, DeepSeek, and Qwen). GPT achieved the highest design success rate at 94.8%, whereas Qwen showed the lowest rate at 50.0%. Across the benchmark dimensions, DoF and controller type exhibited the largest model-averaged variations in design success, with success-rate ranges of 36.3% and 17.6%, respectively, exceeding those associated with system type, coupling level, and damping regime. Comparison of GPT and Qwen showed that their performance gap arose mainly from the control-design knowledge, particularly gain selection and the use of transient-limiting mechanisms. For edge deployment, a specialized 1.5B-parameter model was developed through reasoning distillation. The reasoning-distilled model outperformed the answer-distilled and base model on CoDyControlBench, maintained stable performance across 1-6 DoFs, and achieved successful traget tracking in all three physical trials on a pneumatic-artificial-muscle-driven robotic arm. These results establish a benchmark baseline and highlight the potential of lightweight, edge-deployable controller-design models.

Training controllers that are safe and robust in simulation, and systematically assessing their readiness for real-world deployment, remain key challenges in sim-to-real transfer. To address this, we propose LyEvO, a physics-grounded framework that combines constrained Evolutionary Optimization and Statistical Model Checking (SMC)-based verification with Lyapunov-based stability analysis. Leveraging prior knowledge of the system dynamics, LyEvO uses Lyapunov analysis to compute an initial candidate stability region. An iterative loop then uses operational scenarios drawn from this region to jointly optimize and statistically verify a policy, and subsequently expands the region's boundaries based on the verification outcome. This integrated procedure provides a practical criterion for assessing deployment readiness. We evaluate LyEvO on Cartpole and 3D Quadrotor benchmarks through extensive simulations and targeted real-world experiments, demonstrating safe and robust sim-to-real transfer.

Autonomous agents choose actions using scores that may not reflect experimental success. We developed OPERA, an operator-residual framework for optical experiments. It represents experimental actions as optical operators and evaluates their outcomes using physically interpretable residuals. Operators specify executable changes to measurement, control or reconstruction, while residuals report departures from specified physical conditions. The agent uses both to select, combine or generate operators, and physical performance is evaluated independently against a withheld reference. Across three optical tasks, score-only feedback produced score increases without physical improvement in 23.6--39.0% of decisions, compared with 0.9--1.9% for operator-residual feedback. Operator-residual feedback increased the probability of reaching and maintaining task targets and reduced experimental budgets. Protocols selected in digital twins were transferred to three optical instruments, and repeated experiments showed a lower projection budget in structured-light reconstruction. Together, operators and residuals guide autonomous decisions using measurable physical evidence.

A geometry-conditioned, neuro-symbolic closed-loop architecture is proposed for laser powder bed fusion, in which a standards-aligned ontology operates inside the control loop and couples symbolic reasoning with statistical learning to set the targets of a constraint-aware predictive controller. The ontology links the process objectives and constraints to the signals a controller can observe, and a description-logic reasoner converts them into the references and bounds enforced on each scan. The demonstrated case is overhang dross, a quality limit on the melt pool depth, which governs quality yet cannot be measured during the build, is mapped through a geometry- and power-dependent depth-to-width ratio onto a bound on the observable width, with the ratio and its calibrated uncertainty supplied by a Gaussian process. The reasoner classifies each upcoming feature and selects the active constraints-adding a lack-of-fusion floor at overhangs, a monotone guard beyond the calibrated range, and an energy-density cap where a process window is declared while running only on changes of geometric context and otherwise leaving a single small quadratic program on the per-scan path. In an Eagar-Tsai surrogate calibrated to the NIST AM-Bench benchmark for IN625, the architecture eliminates the dross produced by a geometry-blind controller, holds dross at zero with only a small residual lack-of-fusion under dual scoring, degrades gracefully under deliberate plant mismatch, and retargets to new alloys and constraints by editing ontology data rather than code. The results establish architectural feasibility, experimental calibration of the ratio is the principal next step.

Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian. A k-nearest-neighbor predictor is trained on trajectory histories, the geometric-mean absolute forecast error is evaluated at phase-consistent horizons, and the exponent is obtained from the slope of the logarithmic error profile. Unlike data-driven approaches that reconstruct local evolution matrices or differentiate a learned surrogate, the proposed method extracts the contraction rate directly from out-of-sample forecast errors. Two adaptations are essential: the forecast step is synchronized with the detected orbit period, and candidate slopes are accepted only when they form a stable consensus across several transient lengths. On the logistic map, the method recovers 92 of 112 negative-exponent parameter values with a mean absolute error of 0.0253 and $R^2=0.886$. On a two-dimensional map without fixed points, independent scalar pipelines based on the three observables $x_n$, $y_n$, and $z_n$ give mean absolute errors of 0.00879--0.01145 and $R^2=0.983$--$0.986$. Because the estimation stage uses only observed trajectories, the framework provides a basis for repeated-relaxation experiments in which short sensor responses are available but the governing equations and analytical Jacobian are unknown. Experimental validation remains a subject of future work.

This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers smooth losses with Lipschitz gradient and differences of such losses with convex functions. At each iteration the expected cost is replaced by a sample average that is progressively refined, and the proximal-subgradient stepsize is selected by an Armijo-type line search enforcing a sufficient-decrease property up to stochastic errors induced by the sample-based approximation. This framework accommodates substantially more general problem formulations than existing methods, in particular, it requires neither (weak) convexity of the regularizer nor a uniform bound on the variance of the stochastic oracle, and our analysis yields convergence guarantees that are new even in the smooth setting. Specifically, we establish almost sure convergence of the sequence of function values and stationarity of every accumulation point of the trajectories under the relaxed requirement that the sample-size sequence be merely nondecreasing and unbounded, with no prescribed growth rate. Leveraging the Kurdyka-Lojasiewicz (KL) property, we further upgrade this subsequential guarantee to convergence of the whole trajectory to a single stationary point. Finally, for exponential-type KL desingularizing functions and polynomially growing sample sizes, we derive explicit polynomial convergence rates, up to a logarithmic factor, for both the function values and the iterates.

Control policies optimized in simulation can perform poorly in the real system when the parameters $x$ of the simulator are estimated from limited data but the resulting parameter uncertainty is not represented inside the simulation. A common way to incorporate such ambiguity is to simulate each trajectory of the system under a randomly drawn value for $x$. Since the policy cannot observe the drawn value, it must initially choose controls that perform well across many possible parameter values. However, if the policy progressively observes the system, it can often gradually infer the value of $x$, so that ambiguity vanishes. Over time, the policy then specializes to its estimate of $x$ and loses its robustness. This is undesirable in many real systems, where latent factors are expected to shift. In financial markets, for example, a policy hedging a derivative payoff should remain robust to changes in the volatility regime. To induce such continual robustness, we propose training policies in simulators where ambiguity varies with the system's state but does not systematically decay over time. We formalize this requirement as stationary ambiguity: the simulator should induce a stationary filter process over the latent state. We show how to construct such simulators and demonstrate, on hedging problems, that policies trained under stationary ambiguity preserve robustness to latent factors over time, leading to strong performance on real market data. As a modeling principle, stationary ambiguity informs many simulator design decisions: which models make realistic simulators, how their parameters should be randomized, and how simulator and policy should be initialized. While our experiments focus on hedging, stationary ambiguity may also be useful for other sequential control problems driven by exogenous stochastic processes with shifting latent structure.

Stochastic single shooting trajectory optimization methods such as Model Predictive Path Integral control (MPPI) have been widely adopted in robotics due to their ability to reason about probabilistic dynamics and provide solutions where model gradients are noisy, costly to evaluate, or unavailable. However, satisfaction of terminal constraints when shooting over long action sequences is often sample inefficient, requiring a large number of iterations for convergence. In this paper, we present a stochastic multiple shooting method that optimizes short control action sequences connected via local feedback policies to improve sample efficiency and convergence to a terminal set. Additionally, we show that we are able to synthesize approximate system Jacobians purely from rollouts, making the method suitable for model-based reinforcement learning with black-box dynamics. We demonstrate the algorithm has improved sample efficiency and terminal set convergence for three nonlinear, underactuated optimization problems: a classic cartpole swingup task with analytical dynamics, a cartpole swingup task with learned neural network dynamics, and a VTOL quadplane performing a high angle-of-attack, precision post-stall landing maneuver.