Model Predictive Control

Realistic traffic simulation requires agents that imitate logged behavior and can also be steered along interpretable axes. Such controllability enables engineers to isolate variables, reproduce specific edge cases, and test autonomous systems without real-world risk. We introduce Controllable Neural Variational Agents (CNeVA), a controllable simulated-agent framework that learns to infer a per-agent Gaussian behavior latent from per-channel discounted returns via a closed-form conjugate variational update, conditioning a rectified-flow trajectory generator trained on a mixed channel-mask curriculum for classifier-free guidance. To tackle scarcity in reward signals, we propose soft eligibility gates that replace hard binary thresholds with smooth exponential decay, preserving the gradient signal for near-threshold agents. On the Waymo Open Motion Dataset, CNeVA attains competitive realism on the benchmark while exposing per-channel controllability that the higher-ranked imitation models lack. Speed- and acceleration-based steering produces monotone responses without stall-induced reward hacking. Safety controllability is monotone and substantial with the introduction of soft eligibility. We manage to achieve steerable map compliance under a context-residual return measure. Furthermore, our experiment demonstrates that steering metrics must be read alongside physical-plausibility guardrails to avoid reward-hacking confounds.

This paper presents QuadRocket, a quadrotor-based rocket prototype that provides a low-cost, low-risk platform for validating advanced thrust-vector control strategies for launch vehicle-type systems. The prototype consists of a cylindrical main body mounted on top of a quadrotor through a universal joint, forming a flying inverted pendulum with non-negligible inertia. For control design, the coupled system is modeled as a single axisymmetric rigid body actuated by a vectored force applied along its longitudinal axis. A reduced-attitude representation on the two sphere is adopted to explicitly exploit the vehicle's axial symmetry and to decouple yaw from the thrust-vector direction. On this model, we derive an adaptive backstepping controller that achieves almost global trajectory tracking in the presence of unknown constant disturbances, while a control-point transformation mitigates non minimum-phase behavior. The quadrotor is then treated as a thrust vector actuator, and a dynamic-surface-based attitude controller is designed to track the desired thrust-vector, accounting for actuation dynamics and avoiding explicit differentiation of virtual control signals. The complete architecture is evaluated in simulation and validated experimentally in an indoor motion-capture arena. Results demonstrate accurate trajectory tracking, effective disturbance compensation, and confirm the suitability of the QuadRocket as a versatile testbed for thrust-vector-controlled robotic vehicles.

Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction. Our goal is to achieve sublinear regret with a memory footprint that adapts to the intrinsic complexity of the dynamics rather than the full hidden-state dimension. We focus on the practically central regime of systems with low instability complexity -- eigenvalues outside the real stable interval that do not decay rapidly, together with non-semisimple modes -- potentially embedded in an otherwise stable real spectrum of much higher dimension; we write $k$ for this count. This regime is the primary setting in which stabilization is plausible: we show that many systems with high instability complexity cannot be stabilized without exponentially large controls. Thus, prediction is meaningful for stabilization precisely when the instability complexity is small. Within this regime, we introduce a unified online algorithm that handles every LDS (including non-diagonalizable systems with complex or exploding modes) with a learnable parameter count of $\widetilde{O}(k)$. Finally, we prove a lower bound showing that $k$ is a valid complexity measure: any filter-based predictor needs at least $k$ filters. Experiments corroborate our theory: on a high-dimensional system, our predictor sharply outperforms prior methods at an equal parameter budget.

The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Recently proposed data-driven techniques, like extended dynamic mode decomposition (EDMD), its kernelized variant, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.

We study how to predict the downstream closed-loop performance of a learned latent world model from validation-time diagnostics alone. Choosing the right checkpoint from a world-model training run is difficult: validation loss and multi-step prediction RMSE keep improving long after closed-loop performance has collapsed. We present a suite of structural validation-time diagnostics drawn from optimal-control theory and apply them to Gymnasium's LunarLander v3, which features shaped rewards. We train an RSSM [5, 4] world model on it and treat per checkpoint CEM-MPC return as the oracle for closed-loop quality. By evaluating 40 metrics against this oracle, we find that the strongest single predictor is the Reward Observability Fraction (ROF), which measures the reward predictor's dependence on the observable subspace. We combine ROF with three structural regularizers into a single-number offline checkpoint selection score, the Composite Reward Observability Fraction (CROF). The CROF-selected world model trains a model-based A2C policy that beats a fairly evaluated model-free A2C baseline by ~24.5 return points while using ~65x fewer real-environment interactions, and the same world model also drives a strong zero-shot CEM-MPC policy. Code and data: https://github.com/nsmoly/LunarLander_RSSM.

This paper presents a novel layered planning and control framework based on multi-rate nonlinear model predictive control (MR-NMPC) that enables quadrupedal robots to perform hybrid bipedal locomotion with wall-assisted support in constrained environments. Real-time trajectory optimization for this locomotion presents significant challenges, as the controller must simultaneously plan for both the contact points and the continuous trajectories of the robot's center of mass (CoM) and orientation within the robot's nonlinear dynamics while accounting for unilateral contact constraints, underactuation, and the switching nature of the robot's dynamics. At the high level of the control framework, an MR-NMPC is proposed, which dynamically plans both the discrete-time trajectories of the contact points and the continuous-time trajectories of the CoM and orientation, using a single rigid body (SRB) dynamics model. By incorporating contact-point planning within the multi-rate optimal control framework, this approach enhances dynamic stability compared to heuristic foot placement strategies. At the low level of the control framework, a nonlinear whole-body controller (WBC) based on virtual constraints and a quadratic program enforces full-order dynamics and tracks the MR-NMPC references. The proposed approach is validated through extensive numerical simulations demonstrating the robust wall-assisted bipedal locomotion of a Unitree A1 quadrupedal robot on rough terrains and under external disturbances in a constrained environment. Comparative analysis shows that the proposed MR-NMPC achieves a 2.9 times higher success rate compared to conventional MPC with heuristic-based foot placement strategies in negotiating irregular terrain at high speeds.

Certified world models estimate how long their predictions remain valid. We turn this validity horizon into an operational sensing clock: a rule for when an agent should stop coasting and re-sense. Starting from an audited equivariant world model, we derive a deadline for no-sensing intervals and show that deployable deadlines in learned world models must be drift-aware: on-manifold Lyapunov rates alone overestimate coasting validity, while calibrated native rollout-drift envelopes carry the deployed guarantee. On a frozen 3D VN-JEPA model, the resulting clock controls held-out interval-simultaneous certificate violation across seeds and data shards. In a cue-conditioned theorem-bed (a synthetic bench where all schedulers share the exact model, isolating the scheduling rule), the clock remains valid on the deployment distribution and substantially reduces eventful-tail violations relative to exact-mixture expected-belief scheduling at matched sensing budget. We also report limits: in the short-horizon frozen VN-JEPA regime, empirical conformal horizons match the deployed clock on validity and budget, and a partial-reset exploration finds no clean budget-matched advantage for the spectral term. Thus the contribution is a certified sensing-clock primitive and drift-aware deployment method, not a claim that spectral clocks empirically dominate all non-spectral schedulers.

This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.

World models can enable Model Predictive Control (MPC), but this requires dynamics prediction that is both fast enough for online use and expressive enough to represent uncertain futures. Diffusion models offer a natural mechanism for modeling uncertain dynamics, yet their iterative inference procedure makes them difficult to use for low-latency latent planning. We bridge this gap with Value Diffusion World Models (Valdi), combining end-to-end online training for MPC with a latent diffusion dynamics model. In preliminary experiments on the CarRacing environment, we show that Valdi, using a single diffusion step at both training and inference, matches a deterministic MLP baseline. Our experiments expose a trade-off between predictive multimodality and control performance in this setup. Code is available at https://github.com/Kit115/ValueDiffusionWorldModels.

Robot-environment interactions in dynamic or unstructured settings are often degraded by impact shocks, vibrations, and uncertainties in contact geometry and mechanical properties. This paper proposes an interaction architecture that combines feedback-linearized hybrid position-force control with a passive compliant degree of freedom embedded at the end-effector. Unlike conventional hybrid position-force control, which relies mainly on active feedback, force sensing, and gain tuning, the proposed architecture uses a physical spring-damper interface to store and dissipate impact energy at the contact point before high-frequency shocks propagate to the actuated joints and force-control loop. The approach is evaluated in MATLAB/Simulink on a 2-DOF planar manipulator with three end-effector configurations: rigid, spring-only, and spring-damper. Results under fixed and time-varying interaction conditions show that the spring-damper configuration provides stronger attenuation of contact-induced oscillations, lower force and velocity error variance, and smoother joint-torque response. Representative reductions include 36.5% in fixed-environment tangential force-error standard deviation, 25.4% in variable-environment normal force-error standard deviation, and 41.1% in variable-environment normal velocity-error standard deviation.

We present STT-LfD, a unified Learning from Demonstration (LfD) framework that integrates motion learning with control for unknown Euler-Lagrange systems. Unlike traditional decoupled approaches that track a fixed reference, the proposed method treats demonstrations as a data-driven safety specification. Using heteroscedastic Gaussian Processes, STT-LfD learns Spatiotemporal Tubes (STTs) as an intent envelope that capture time-varying precision requirements of a task. A closed-form feedback controller then enforces these learned constraints while respecting actuator limits, without requiring explicit system identification. The approach preserves the temporal structure of demonstrations, remains computationally efficient, and avoids explicit system identification. Hardware experiments on a mobile robot and a 7-DOF manipulator show that it outperforms baselines in robustness to disturbances and computational speed.

Redundant robotic manipulators operating in constrained and human-interactive environments require accurate task-space tracking together with rigorous safety guarantees under dynamic uncertainties. Classical operational space computed torque controller (OSCTC) relies on accurate dynamic models and degrades in the presence of disturbances. In contrast, the data-driven paradigm of residual learning approximates disturbances as functions learned from full-state measurements, which are often noisy in practice, lack rigorous theoretical guarantees, and introduce additional design complexity. This paper proposes a robust OSCTC framework that integrates an extended state observer (ESO) with conformal prediction to combine model-based robustness and data-driven adaptability. The ESO estimates lumped disturbances directly in operational space without requiring full-state measurements as in residual learning, and a robust control barrier function (CBF) is constructed to enforce safety under uncertainty. However, robust CBFs require a known disturbance-variation bound to guarantee absolute safety, which often leads to conservatism in practice. To address this limitation, we further employ a sliding-window conformal prediction mechanism to estimate the bound online in a distribution-free manner, thereby achieving practical probabilistic safety guarantees. Experiments on a 7-DoF Franka Research 3 manipulator demonstrate millimeter-level tracking accuracy and real-time safe control at 1~kHz under various disturbances.

Autonomous agents, whether LLM-driven software agents or robotic physical agents, face a common class of failure modes when operating without continuous human oversight: safety violations from unverified actions, behavioral instability from unconstrained loops, and continuity loss from unhandled error states. We develop \system{}, a discrete-time control system that combines five execution gears (\Gobs{}, \Gsug{}, \Gplan{}, \Gexec{}, \Gint{}) with utility-gated dispatch and event-driven fallback. For the single-agent case, we prove monotonic stability, execution safety, eventual stabilization, fallback completeness, and equivalence to a gear-constrained Markov decision process. For multi-agent cyber-physical systems (CPS), we apply the established \smart{} managed-autonomy lifecycle and map runtime evidence into its four governance states (\Stable{}/\Meta{}/\Assisted{}/\Regulated{}). Consensus gating, swarm-level Lyapunov analysis, per-agent gear authority, and rendezvous control provide distributed safety and stability guarantees, including zero collision under the stated assumptions. We evaluate the resulting runtime on a three-agent UR5 robotic assembly cell using fault magnitudes calibrated from the NIST \emph{Degradation Measurement of Robot Arm Position Accuracy} dataset across 10,000 Monte Carlo episodes. It achieves a 99.6% anomaly detection rate versus 2.1% for the single-agent baseline, reduces detection latency by $3.5\times$, and supplies a formal physical-workspace safety certificate. The execution gears act as micro-level permissions beneath the \smart{} runtime governance states, separating action control from autonomy governance.

Latent world models enable planning from high-dimensional observations by predicting future states in a compact latent space. However, these models are typically kept frozen at test time: when their predictions become inaccurate, planning can fail, especially under test-time distribution shift. To address this, we propose AdaJEPA, an adaptive latent world model that performs test-time adaptation within the closed loop of model predictive control (MPC). After training, AdaJEPA plans and executes the first action chunk, uses the observed next-state transition as a self-supervised adaptation signal, and replans with the updated model. This closed-loop update continuously recalibrates the world model without additional expert demonstrations. Across a range of goal-reaching tasks, AdaJEPA substantially improves planning success with as few as one gradient step per MPC replanning step.

This paper presents a novel non-linear mathematical model of an articulated tractor-trailer system that can be used, in combination with receding horizon techniques, to improve the performance of path tracking tasks of articulated systems. Due to its dual steering mechanisms, this type of vehicle can be very useful in precision agriculture, particularly for seeding, spraying and harvesting in small fields. The articulated tractor-trailer system model was embedded within a non-linear model predictive controller and the trailer position was monitored. When the kinematic of the trailer was considered, the deviation of trailer's position was reduced substantially alongside not only straight paths but also in headland turns. Using the proposed mathematical model, we were able to control the trailer's position itself rather than the tractor's position. The Robot Operating System (ROS) framework and Gazebo simulator were used to perform realistic simulations examples.

The control of agile quadrotors in dynamic and uncertain environments remains an open area of investigation to this day, particularly when the complete system dynamics are partially known or highly nonlinear. This work introduces a novel machine learning-based feedback-linearization control framework that employs a Gaussian Radial Basis Function (RBF) neural network (NN) to model and compensate for unmodeled dynamics in real time. The proposed controller leverages the universal approximation capability of RBF networks to model nonlinearities and uncertainties. An online adaptation of the RBF NN updates the network's weights without prior training. The control law is derived using the Lyapunov stability theory, herein guaranteeing closed-loop stability and providing theoretical guarantee of asymptotic convergence of a trajectory tracking task. Gazebo simulation and real flight experiments are conducted using the Bitcraze's Crazyflie 2.1 quadrotor subject to unmodeled air drag, actuator dynamics, and external disturbance. Despite incomplete knowledge of prior dynamics and presence of external disturbance such as air drag and drift in state estimation, the proposed controller improves trajectory tracking with rapid convergence and reduction of position-norm and yaw orientation RMSE by more than $7.13\%$ and $49.27\%$ respectively compared to baseline feedback linearization controller.

Accurate 4D trajectory prediction and closed-loop tracking are essential for Unmanned Aerial Vehicle (UAV) swarms to achieve safe and efficient operations in complex low-altitude environments such as urban airspaces, industrial sites, and indoor facilities. However, this task remains challenging due to intrinsic nonlinearity of UAV swarm dynamics and strict real-time constraints of swarm formation control. To address these challenges, we propose a unified framework that couples coarse-to-fine trajectory forecasting with uncertainty-aware Distributed Nonlinear Model Predictive Control (DNMPC). Our approach features two key innovations: 1) a dimension-decoupled trajectory prediction module that reduces computational complexity by forecasting axis-wise motion, and 2) a diffusion-based residual dynamics refinement module that captures temporally correlated dynamic uncertainties. These refined predictions are then integrated into a DNMPC loop to ensure formation stability. We also introduce a synchronized multi-scenario 4D UAV swarm dataset spanning six representative airspace scenarios. The dataset contains over \textbf{7,900} frames of synchronized three-UAV trajectories with frame-level annotations of speed intention and target sector. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines, reducing trajectory tracking error by up to \textbf{10-15%} and achieving sub-\textbf{0.07,m} average tracking error in complex urban and industrial environments, while maintaining real-time inference speeds of 34 FPS (sub-30 ms latency) suitable for agile flight.

Adaptive agents are usually judged by what they do, but an agent can appear stable while the internal effort required to keep it stable is increasing. This hidden regulatory burden matters for artificial agents operating under noise, delay, or changing demands: two systems may reach similar internal states while one requires much more corrective control to get there. Here, we study whether that burden depends on history. Using a computational model of adaptive uncertainty regulation, we drive an artificial agent through a continuous change in its uncertainty target and then reverse the change without resetting the agent. This creates a simple test for carryover: does the controller respond only to the current target, or does the path by which the agent reached that target still matter? The simulations show a clear history-dependent effect. The adaptive gain required to regulate the agent forms a reproducible hysteresis loop, meaning that the same target can require different levels of control depending on whether the agent is moving toward or returning from a more demanding regime. The timing of regulation also matters. When stabilization is available before disturbance exposure, the agent generally requires less adaptive gain than when it can only recover after disturbance has already acted. The state-level coherence measure also shows path dependence, but the timing effect is much clearer in regulatory gain. The main difference is therefore not that anticipatory regulation produces a completely different state. Rather, it reaches comparable regulated behavior with lower modeled control demand. These results suggest that adaptive agents should be evaluated not only by whether they remain organized, but by how much regulation they must recruit to do so.

While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints. Existing work often treats safety as a metric to optimize for, which competes with other performance objectives, if training converges at all. Instead, we introduce ShardNet, a neural network architecture that strictly enforces unions of polyhedral constraints by construction, using a differentiable projection layer parameterized by a classification network. The key insight is to embed safety into the neural network's structure, allowing performance to be optimized independently because formal safety guarantees are always given. In contrast with existing neural architectures that can only enforce simple convex constraints, ShardNet enables the first safe-by-construction synthesis of forward-invariant neural network controllers on closed-loop systems where safety constraints are expressed as nonconvex unions of polyhedras or learned value function level sets. To support this, we also introduce a technique to verify and train such value functions correctly as rectified linear unit (ReLU) networks, which has not previously been possible. On double integrator benchmarks drawn from the literature, ShardNet policies maintain 100% safety on verified sets and achieves significantly lower objective loss compared to existing formal methods. Furthermore, our value function training technique also produces safe sets more than 3 times larger than existing verification approaches.

We study a finite-state symbolic controller for systems in which the admissible visible transitions are fixed in advance and each visible state carries a minimum dwell requirement. The resulting model, which we call a destination-labeled self-looping system with dwell (DLSL system), records the visible graph together with local decision maps; dwell memory appears only after phase expansion. The main structural issue is that, once dwell is imposed, the current visible state no longer determines whether a departure is allowed. This leads to the converse problem: which deterministic transducers arise as phase-expanded realizations of DLSL systems over a fixed visible graph? We show that the answer is exactly the class of fiber-linear graph-respecting transducers. Under natural reachability and realizable-departure assumptions, equivalent accessible realizations over the same visible graph are isomorphic; in particular, the visible transduction determines the dwell vector and the local decision maps. We also prove that any graph-preserving deterministic realization enforcing dwell values $(d_i)$ requires exactly $\sum_i d_i$ control states. Finally, we give an $O(|Q||Ω|)$ recognition and reconstruction procedure, and extend the analysis to an edge-entry variant in which transitions may enter interior phases of successor fibers.

Time Window Temporal Logic (TWTL) is a rich specification language for cyber-physical systems that can compactly express sequential tasks with explicit timing constraints. In this paper, we consider the problem of synthesizing control inputs for discrete-time linear systems subject to TWTL task specifications. Building on the quantitative semantics (robustness) recently introduced for TWTL in [1], we encode the robust satisfaction of a TWTL formula as a set of Mixed-Integer Linear constraints and pose synthesis as a Mixed Integer Linear Program (MILP) that maximizes the robustness degree. We prove that any feasible solution with positive objective value guarantees Boolean satisfaction of the specification. We address two synthesis settings: an \emph{open-loop} formulation that optimizes the full control sequence from the initial state, and a \emph{closed-loop} receding-horizon Model Predictive Controller (MPC) formulation that re-solves the MILP at each step using the current measured state. A key feature of our MPC formulation is a \emph{task-adaptive horizon} that exploits the TWTL Deterministic Finite Automaton (DFA) to determine the active sub-task at each step, limiting the prediction horizon to the remaining window of the current task rather than the full formula horizon, this makes each re-solve significantly cheaper than the initial open-loop solve.

The increasing integration of Electric Vehicles (EVs) has imposed a growing harmonic challenge on the power grid. For AC/DC Power Factor Correction (PFC) in single-phase On-Board Chargers (OBCs), Model Predictive Current Control (MPCC) improves the current quality by predicting and tracking the inductor current. However, finite control set MPCC selects switching states, resulting in discrete control actions and a limited optimisation space. Moreover, the MPCC cost function based on instantaneous current tracking error has limited capability to compensate for low-order harmonic disturbances induced by dead time, control delay, and model parameter mismatch. This paper proposes a duty cycle predictive MPCC incorporating a real-time harmonic estimation reference. The proposed method dynamically estimates the low-order harmonic components of the input current and corrects the MPCC reference current, enabling continuous duty cycle control and targeted suppression of dominant low-order harmonics. Simulation results on a single-phase OBC demonstrate that the proposed duty cycle predictive MPCC reduces the steady-state current THD_i from 11.47% to 6.10% compared with the switching state predictive MPCC. With the harmonic reference, the THD_i is further reduced to 2.85%.

Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging. In this work, we treat such training trajectories as temporal networks and apply recently proposed strategies for the scalar embedding of temporal networks. We investigate whether such a scalar embedding provides a meaningful low-dimensional representation of neural network training dynamics. Using a multilayer perceptron trained on the MNIST classification task, we show that the embedding preserves the main dynamical features observed in the original parameter space, including the emergence of sensitivity to initial conditions for specific learning rate regimes and an accurate reconstruction of the network's maximum Lyapunov exponent. We then use the embedded scalar trajectory to define a characteristic time, analogous to a Lyapunov time, after which the exponential separation between initially close embedded trajectories saturates. This characteristic time captures the typical decorrelation time between initially close network trajectories in the original high-dimensional system. Finally, we investigate the statistical organization of asymptotic training states through a spacing observable defined in the embedded space. We find that the distributions of rescaled asymptotic spacings collapse onto a common form across initial conditions and are compatible with a skew lognormal distribution. Altogether, our results suggest that scalar low-dimensional embeddings provide a useful framework for studying and visualizing the dynamical properties of neural network optimization trajectories.

Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which -- while potentially sub-optimal for the task at hand -- can be rapidly implemented. For the numerical solution of ill-conditioned linear systems of equations, the standard solution for prototyping is Tikhonov-regularised inversion using a nugget. However, selection of the size of nugget is often difficult, and the use of data-adaptive procedures precludes automatic differentiation, introducing instabilities into end-to-end training. Further, while data-adaptive procedures perform multiple linear solves to select the size of nugget, only the result of one such solve is returned, which we argue is wasteful. This paper aims to circumvent the above difficulties, presenting autonugget; a Python package for automatic and stable numerical solution of linear systems suitable for rapid prototyping, and fully compatible with automatic differentiation using JAX. autonugget combines multiple linear solves using Richardson extrapolation to determine the solution of the ill-conditioned system, improving in accuracy over approximations based on a single nugget.

Modeling tethered space systems is critical for advanced orbital operations. Flexible components such as tethers and space nets are integral to these systems but present significant control challenges due to their high dimensional, strongly coupled, and nonlinear dynamics. While data driven methods offer alternative modeling approaches, they frequently struggle with long term predictive stability and spatial generalization. To address this, we propose the Koopman Graph Dynamics (KGD) framework to learn the structural dynamics by integrating the global linear evolution of the Koopman operator with the local topological priors of Graph Neural Networks. Building upon this representation, we develop a KGD based Model Predictive Control strategy for tethered space systems. Subsequently, the ground experiments on flexible tether and space net demonstrate the high precision modeling capabilities of the proposed method. Crucially, the framework exhibits exceptional capacity for spatial transfer without retraining. Models trained exclusively on small configurations successfully predict and control significantly larger, unseen physical scales. Furthermore, the orbit simulations within a physics engine verify the effectiveness of the proposed approach for tethered space systems.

In this paper, we develop a fractional stochastic neural network with residual dynamics driven by fractional Brownian motion. By introducing a discrete stochastic maximum principle for the network, we construct the corresponding adjoint recursion. For deterministic network parameters, we prove mean square convergence of projected samplewise stochastic gradient descent. Numerical experiments include a closed form convergence test, noisy regression with uncertainty quantification, long memory time series generation and image classification under structured perturbations. The results identify settings in which fractional drivers improve long memory recovery or robustness relative to Brownian and deterministic baselines.

Artificial neural networks (ANN) provide accurate continuous-valued representation, whereas spiking neural networks (SNN) offer event-driven temporal processing, yet both paradigms face limitations when value encoding and timing dynamics must be learned within a single computational structure. This paper introduces a network based on Unified Complex-valued Neuron (UCN), a new neural computational model that integrates continuous activation and phase-driven event generation through an asymmetric complex-valued state. In the UCN, magnitude encodes signal strength while phase governs intrinsic temporal evolution and valued spike emission. A foundational training framework combining backpropagation (BP) and backpropagation through time (BPTT) is first developed to optimize magnitude and phase pathways in a unified way. To reduce computational complexity, an event-driven adaptive phase learning (EAPL) rule is then introduced as a more efficient alternative. The proposed model is evaluated through object tracking and Lorenz attractor learning. Results demonstrate that UCN-based Network (UCNN) provides accurate, stable, and interpretable spatiotemporal learning while preserving sparse event-driven computation for neuromorphic and edge-AI applications.

Benefiting from the strong ability to capture data distributions, diffusion models have become powerful tools for solving image inverse problems. The key is to controllably steer the sampling trajectory toward the measurements while respecting the diffusion prior. In this work, we introduce Stochastic Optimal Control Sampling (SOCS), which models the denoising process as a dynamical system and injects control signals via SOC. Previous SOC-based approach addresses inverse problems by optimizing over the entire trajectory, which is computationally expensive. In contrast, we derive a closed-form control update and apply it at each sampling step, pulling the measurement-consistent clean prediction back onto the denoising flow. In SOCS, we can readily modulate the control strength to align with the diffusion model's native capabilities and thereby enhance perceptual quality. Our method is compatible with a variety of linear stochastic differential equation backbones. Extensive experiments across a broad spectrum of image inverse tasks demonstrate that SOCS achieves accurate measurement-aligned reconstructions with improved visual fidelity and stronger quantitative performance.

Stackelberg differential games (SDGs) provide a powerful framework for hierarchical decision-making in stochastic and continuous-time environments, yet their solution remains computationally challenging due to the complexity of traditional dynamic programming and Hamilton-Jacobi-Bellman-Isaacs (HJBI) methods, especially in high-dimensional systems. This paper proposes an entropy-regularized reinforcement learning (ERRL) approach for linear-quadratic SDGs (LQ-SDGs) within a continuous-time diffusion framework governed by Markovian regime switching. The key innovation lies in deriving exploratory weakly-coupled HJBI equations with entropy regularization, which promotes stochastic policies that actively avoid suboptimal equilibria -- a limitation of classical SDG methods. Neural networks are integrated to approximate regime-dependent value functions and solve high-dimensional partial differential equations (PDEs) efficiently, while a novel sampling technique enhances computational tractability. Numerical results demonstrate the effectiveness of the framework compared to conventional approaches, particularly in escaping suboptimal traps through exploratory policies. The study highlights the critical role of entropy regularization and neural network approximations in achieving robust solutions for hierarchical decision-making problems under abrupt environmental shifts.

To address parameter misspecification and sudden structural environmental changes in conventional stochastic differential game (SDG) frameworks, this paper introduces a distributional control approach that characterizes optimal strategies as probability distributions over actions, conditioned on the continuous state, the discrete regime state, and parameters. This forms a reinforcement learning framework for entropy-regularized zero-sum stochastic differential games (ERRL-ZSSDGs) in a regime-switching jump-diffusion process. Using the dynamic programming principle (DPP), we derive the associated coupled systems of Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, from which equilibrium strategies are expressed via gradients of the value function. For linear-quadratic problems, semi-analytical solutions for both value function and equilibrium strategies are obtained by solving a system of coupled ordinary differential equations (ODEs). In more general settings, an Actor-Critic policy improvement algorithm is developed to approximate the value functions and equilibrium policies across different regimes. The method is applied to an investment game, and numerical examples illustrate the effect of the temperature parameter and regime transitions on optimal policies and values.

The cart-pole swing-up is a canonical benchmark for nonlinear control of underactuated systems, yet an end-to-end guarantee linking the global swing-up maneuver to the local stabilizer is seldom formalized. We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium from a compact set of initial conditions. The swing-up law is derived from an energy-error Lyapunov function; canceling the autonomous conservative term yields a strictly sign-definite Lyapunov derivative, and convergence follows from LaSalle's invariance principle. We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence. For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition. Numerical simulations corroborate the theoretical analysis.

Model Predictive Control (MPC) is the standard predictive layer in hierarchical quadruped controllers, but the per-cycle QP solve limits the update rate achievable on embedded processors. Because legged gaits revisit a bounded region of state space, MPC solutions admit caching and reuse. This paper proposes \emph{Certified CacheMPC}: a Locality-Sensitive-Hashed cache of horizon contact-force trajectories, partitioned by contact mode, retrieved at query time and accepted only when an a-posteriori per-query certificate confirms primal feasibility and a Lagrangian dual-gap upper bound on cost suboptimality. A bounded-budget controller schedule combines top-$K$ certified retrieval, a deadline-bounded QP solve, and a shifted last-certified fallback. The framework is evaluated on a Unitree Go2 across $2{,}038$ usable cold-controller MuJoCo trials, including a $600$-trial $n\!=\!50$ campaign at three failure-boundary cells, and a first-deploy session on the on-robot NVIDIA Orin NX. The un-gated cache delivers a $25\times$ median solve-time speedup in simulation and an $18.7\times$ median speedup on hardware. At $n\!=\!50$ no statistically significant difference in closed-loop stable rate is detected between the cache variants and the no-cache baseline at any tested cell. The certificate's contribution to closed-loop safety is not resolvable at the present sample size.

PAC-Bayesian bounds provide finite-sample guarantees for data-dependent randomized predictors, but applying them to learning-based control is difficult because the natural objective is a quadratic trajectory cost. Such losses are unbounded, non-Lipschitz , and lead to response-dependent Chernoff terms. We employ System Level Synthesis parameterization, which exposes the closed-loop trajectory map of a linear system directly and makes the quadratic control loss amenable to explicit certification. Moreover, we provide a set of PAC-Bayes-Chernoff certificates for posterior distributions over feasible closed-loop responses. For Gaussian disturbance trajectories with arbitrary covariance, we derive an exact one-sided Gaussian transform and a tractable quadratic upper bound expressed through closed-loop sensitivity quantities. We also derive a posterior-localized surrogate for settings where pointwise closed-loop response certificates are unavailable or have support related admissibility issues. Although PAC-Bayes certifies a non-degenerate posterior, the convex quadratic form of the SLS loss transfers the certificate to the posterior mean response. We present a deterministic mean response deployment result that is particularly suitable for control while retaining the stochastic posterior in the bound. Additionally, we provide a data-driven bound for this deployment, transitioning away from an oracle bound. Minimizing this bound naturally results in a learning algorithm for control selection from data. Numerical experiments on a double integrator show that the algorithm acts as a sensitivity-aware finite-sample regularizer, improving held-out cost and reducing closed-loop sensitivity in the low-data regime

High-precision humanoid control is limited by target-domain dynamics mismatch, where the same control objective can induce different realized motions under changes in terrain, payload, or actuator response. Existing methods either pursue zero-shot transfer through domain randomization or in-context adaptation without target-domain specialization, or require heavy adaptation pipelines that leverage target-domain data, such as model calibration, residual learning, or policy retraining. In this paper, we present FADA (Few-Shot Domain Adaptation via Dynamics Alignment), a three-stage Planner-Inverse Dynamics Model (Planner-IDM) framework for few-shot adaptation in humanoid control. FADA first trains an oracle policy with privileged information and then distills the oracle behavior into a deployable Planner-IDM student through DAgger. At deployment, FADA freezes the planner and finetunes only the IDM using approximately 2 minutes of target-domain rollouts with standard supervised learning. Rather than requiring optimal demonstrations or rewards, FADA uses the paired actions and observations that are observed during these rollouts as supervision, aligning the IDM's action generation with target-domain dynamics. Experiments show that FADA outperforms both in-context and end-to-end adaptation baselines, improving task performance under dynamics shifts and enabling real humanoid robots to execute diverse high-precision whole-body tasks. Implementation details and qualitative hardware rollout videos are available at https://lecar-lab.github.io/FADA-humanoid/.

Autonomously controlling and handling a vehicle at and beyond its stability limit is a mathematically and computationally demanding task. Prior demonstrations of automated drifting have been limited to research platforms with instantaneous torque delivery and independently actuated wheels, leaving their applicability to production vehicles with actuator latencies and mechanically coupled axles uncertain. To overcome these issues, we design a predictor to compensate for powertrain delays, develop a revised control formulation to accommodate higher actuation latencies as well as a differential coupling on the driven axle, and introduce brake-based velocity stabilization. This paper presents the controller framework, the model extensions, and real-world experimental results. We observe that our controller enables a production sports car with a combustion engine to robustly sustain circular and figure-eight drifts, limiting lateral error to 1.1 m and sideslip overshoot to 0.06 rad despite actuator delays exceeding 250 ms, while mitigating oscillations and maintaining stable path and sideslip tracking. In conclusion, our results establish that autonomous drifting is feasible on production-ready vehicles, opening pathways to advanced safety systems capable of stabilizing cars in scenarios where traditional control fails.

This work studies resilient output containment for heterogeneous linear multi-agent systems with actuator cyber-attacks over directed network topologies. The leaders generate bounded locally absolutely continuous trajectories; however, their dynamics, velocity bounds, and motion envelopes are undisclosed to the followers. The cyber-attack model includes state- and input-correlated, as well as bounded exogenous actuator false-data terms. A continuous two-layer adaptive control architecture is proposed. The first layer is a virtual-actuator reconfiguration layer that uses partial state measurements to compensate for actuator attacks in the local tracking-error dynamics. The second layer is a network interface that generates task-space commands via an adaptive interaction protocol. This protocol uses only neighbor-exchanged network-interface states whose dimensions match those of the plant output, and it does not require global graph knowledge for parameter tuning. For directed graphs, under a leader-rooted united spanning-tree condition, a nonsmooth Lyapunov analysis yields asymptotic containment at the command level. The physical outputs then converge to the leader convex hull up to a residual determined by the command-tracking local controllers. Simulation results using a network of quadrotors with damped suspended loads illustrate the performance of attack recovery and containment tracking.

This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on $\mathcal P_2(\mathbb R^d)$, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available. On the other hand, a direct reduction to a time-discrete Bellman equation avoids the non-identifiability issue but loses the differential equation structure. To bridge these two viewpoints, we introduce a Mean-Field-PhiBE (MF-PhiBE), which incorporates discrete-time transition information into a continuous-time PDE on the Wasserstein space. The MF-PhiBE replaces the unknown infinitesimal drift and covariance in the policy-evaluation equation by one-step estimators computed from data, while preserving the generator structure of the McKean-Vlasov HJB equation. We also derive a policy-gradient theorem for entropy-regularized randomized feedback policies, expressing the actor direction through an action-wise infinitesimal advantage and the score of the policy. Combining these two ingredients yields a model-free actor-critic method. We prove a first-order consistency estimate showing that the value induced by an optimal MF-PhiBE policy approximates the optimal continuous-time value with an error of order $Δt$. In the linear-quadratic case, we show our approximation achieves second-order accuracy with only one-step data. Numerical experiments on an LQR benchmark and a crowd-aversion problem illustrate the proposed framework.

This paper presents a hierarchical control framework using model predictive control (MPC) and reinforcement learning (RL) for active roll control to manage lateral load transfer during autonomous racing of a wheeled quadruped. The framework integrates offline time-optimal raceline generation, an online MPC planner that actively minimizes the lateral Load Transfer Ratio (LTR), and a low-level, whole-body RL policy deployed directly onto the robot's 16 actuators. The MPC is based on a vehicle dynamics bicycle model of the Unitree Go2-W platform. The robot's leg actuators act as active suspension where knee joints generate anti-roll torque to bank into turns. Physical track experiments demonstrate that active roll control reduces mean LTR by up to 44%, improves the fastest lap time by 8.7%, and boosts peak lateral acceleration capability by 21.3% to 1.98 $m/s^2$, maintaining robust high-speed stability beyond the range of a non-tilting baseline controller. Supplementary code and video can be found at https://github.com/meisman-ucb/go2w-roll-control-mpc

Soft robots are challenging to control due to their nonlinear and time-varying dynamics. Data-enabled predictive control (DeePC) offers a model-free alternative by directly leveraging measured input-output trajectories to construct a predictive controller. However, its receding-horizon formulation requires solving a constrained optimization problem at every sampling instant, which can be computationally demanding for real-time deployment on resource-limited robotic platforms. To address this limitation, we propose an adaptive reinforcement-learning-based event-triggered DeePC (RL-ET-DeePC) framework for soft robotic control. A model-free RL policy is trained to determine when to invoke the DeePC optimizer based on the current system state representation, thereby reducing unnecessary optimization calls while preserving closed-loop performance. Simulation results show that RL-ET-DeePC reduces optimization frequency by up to 66% compared to periodic DeePC, while maintaining comparable tracking accuracy. Hardware experiments on a three-dimensional cable-driven soft robotic arm demonstrate zero-shot transfer, achieving a 34% reduction in optimization frequency with tracking accuracy comparable to periodic DeePC and more consistent performance than a static threshold-based event-triggered baseline.

A key step toward autonomous industrial operation is the ability to create and reconfigure control policies from natural-language requirement specifications, with minimal or no manual redesign. In this setting, policy generation by AI agents can be a credible path when paired with a plant-aware validator (e.g., a digital twin) that can check generated candidate actions before execution. However, practical deployment is constrained by inference latency and compute footprint: large cloud-based models are often too slow, opaque, or data-sensitive for edge closed-loop use. This work investigates whether a compact Small Language Model (SLM) can be retrained for control reasoning and embedded in a validator-guided correction loop. We use a Qwen2.5-1.5B model aligned via Group Relative Policy Optimization (GRPO), combined with (i) an action agent, (ii) a symbolic/digital-twin-style validation layer, and (iii) a reprompting agent that iteratively steers outputs toward valid actions. In randomized thermal-control simulations (30 experiments with 500 steps each), the framework achieves 91.5% average action-alignment accuracy (86.3%--100% across cases) at 3.84,s mean inference latency. Under symbolic re-mapping, it maintains a 95% in-range rate, indicating robust physical regulation despite reduced token-level agreement. These results support SLM+validator architectures as a practical path toward reconfigurable autonomous control at the edge.

Learning-based Lyapunov Control (LLC) provides formal stability guarantees for nonlinear systems, but its validity relies heavily on accurate system models. Parameter variations and uncertainties may invalidate stability constraints, leading to costly retraining. Although D-learning can estimate Lyapunov derivatives without relying on explicit dynamics models, it remains limited by single-task dynamics and degrades under large parameter shifts. We propose Reptile-D-learning, a framework that leverages the Reptile meta-learning algorithm to capture shared dynamical structures across systems with different parameters, thereby learning a generalizable Lyapunov network initialization and a high-performance controller. Experiments on multiple nonlinear control systems demonstrate that Reptile-D-learning significantly improves both generalization and rapid adaptation to unseen parameter configurations.

Large language models (LLMs) can improve autonomous driving planning but are costly to query online, and existing fast-slow planners often rely on hand-designed triggering rules that either over-call the slow system or call it at the wrong times. We formulate slow-system invocation as a resource-aware sequential decision problem and propose the Adaptive Slow-System Control Gate (ASSCG), which makes frame-level Query/Cache/Drop decisions to refresh, reuse, or suppress slow guidance. ASSCG uses an RWKV backbone for efficient long-horizon gating and is trained with supervised fine-tuning followed by GRPO-style compute-aware reinforcement fine-tuning. We apply ASSCG to two different fast-slow architectures: (i) AsyncDriver on nuPlan Hard20 closed-loop evaluation, where ASSCG improves score to 67.28 (+2.28) while reducing average end-to-end inference latency by 60%; and (ii) a RecogDrive-based dual system that we build by replacing its original VLM-2B module with a lightweight ViT-based fast planner and adding an LLM slow planner, evaluated on NAVSIM, where ASSCG achieves 91.4 PDMS (+0.6) and increases average speed by 25%. The project page, including video visualizations and additional results, is available at https://williamxuanyu.github.io/asscg/.

Runtime assurance (RTA) protects a safety-critical system by switching from an advanced controller to a verified safe controller when a monitored condition is violated. The standard latching rule, which trips on the first breach of the safe set and then coasts, is correct for a diverging controller but pathological for a capable online-adapting one. Such a controller is unsafe by design during a bounded recovery transient. It must excite the plant to identify the fault before it can correct it, so a latching shield trips on that transient and suppresses a controller that would have recovered. We introduce the conformal recovery-deadline certificate, a split-conformal, distribution-free, finite-sample upper bound on the adapting controller's recovery time that licenses delayed fallback with a coverage guarantee, backstopped by a verified monitor at a hard critical limit. The certified deadline discriminates capable from incapable controllers, keeping the recoverer autonomous while catching the diverger. The construction separates autonomy, governed by statistical coverage, from safety, governed by the verified backstop, as an instance of reliability-asymmetric design. We prove marginal coverage, a weighted extension that restores coverage under a known fault-distribution shift, and group-conditional Mondrian coverage. We demonstrate all three on two unrelated Simplex testbeds: a 6-DOF spacecraft attitude controller and a torque-controlled inverted pendulum. Both show the same suppression pathology and the same cure, making the certificate a domain-general mechanism rather than a single-system trick.

Safe control has been widely studied in various safety-critical applications, for instance, autonomous driving. In order to ensure the autonomous vehicle does not collide with other vehicles, it is essential to obtain an accurate expectation of surrounding vehicles' behavior and react adaptively. Instead of assuming fully cooperative and homogeneous vehicles using the same safety-critical controllers, recent works have been exploring different data-driven approaches to model the neighboring vehicles' underlying controllers with observed data. However, existing works either suffer from 1) the inter-vehicle influence during the multi-vehicle interaction, which makes it hard to determine the causality of surrounding vehicles' behavior in controller modeling, or 2) being dominated by the worst-case analysis, which may lead to overly conservative behavior. In this paper, we extend the prior work on Parametric-Control Barrier Function (Parametric-CBF) to multi-robot interactions with embedded causality inference to explicitly reason over the inter-vehicle influence. Given the learned Causality-based Parametric-CBF, we present an adaptive safety-critical controller that allows the ego vehicle to safely react to surrounding vehicles with the learned expectation. We demonstrate that by leveraging the motion flexibility among multi-vehicle systems, task efficiency can be greatly improved in various interaction-intensive scenarios.

Humanoid robots require whole-body controllers that are both robust and precise in contact-rich environments. While deep reinforcement learning (RL) achieves robust stability, its behavior is tightly coupled to the training objective and command interface, making it difficult to add new feedback objectives without retraining. In this study, we propose an RL guided whole-body model predictive path integral (MPPI) framework that acts as an add-on feedback controller on top of a pretrained RL policy. Instead of using RL policy as the final controller, we use it as a sampling prior that biases MPPI rollouts toward dynamically feasible behaviors. Task objectives are specified through modular MPPI cost terms, and MPPI closes the loop by continuously correcting the RL prior online to satisfy these objectives without retraining the policy. Simulations on a 29-DoF Unitree G1 humanoid in MuJoCo demonstrate stable high-rate control (average 280~Hz). The proposed method improves task-level precision over a pure RL baseline under the same command interface. This is achieved by correcting systematic drift during straight walking and tracking additional whole-body reference signals imposed through the cost.

Many modern Language Model (LM) pipelines return an averaged model, such as an exponential moving average of the training iterates, rather than the final iterate itself. This raises a fundamental question: given that we will return an iterate average, how should we change training to improve the performance of this average? We study this question by formulating optimizer design for the iterate-average estimator as an optimal-control problem. In a continuous-time stochastic quadratic model, we solve for the control strategy that minimizes the error of the returned average subject to a penalty on the size of the intervention. A practical approximation to this controller yields PACE, a lightweight wrapper around AdamW that pulls the live weights toward their exponential moving average with a clipped, per-coordinate control strength. We prove that a stylized version of PACE converges at the standard stochastic convex optimization rate, up to a factor depending on the averaging rule, while in the quadratic setting it can strictly improve the limiting squared error of the iterate-average estimator and can do so by an arbitrarily large factor on some instances. Empirically, our results suggest that PACE improves over AdamW and EMA-evaluated AdamW in supervised fine-tuning of 1-2B parameter LMs and in GPT-2 pretraining on FineWeb for a wide range of learning rates, decay schedules, and other hyperparameters.

Model Predictive Control (MPC) is widely used in industrial and robotic systems for enforcing constraints and embedding domain knowledge through finite-horizon optimization-based planning. However, despite these strengths, an MPC scheme typically does not yield optimal policies for sequential decision-making problems formulated as Markov Decision Processes (MDPs). Recent combinations of MPC with Reinforcement Learning (RL) alleviate this issue by treating MPC as a parameterized model of the optimal policy of an MDP and adjusting its parameters using data. While these approaches typically consider classical MDPs, many real-world problems include future information--such as forecasts, prices, or reference trajectories--at decision time, which must be included in the MDP state for optimal decision-making. Current MPC-RL approaches do not directly account for this augmented-state structure, raising the question of how to incorporate future information into MPC to obtain an optimal policy. This work establishes the structural requirements under which a parameterized MPC can exactly represent the optimal value functions and policy of an MDP with future information. We further demonstrate that such a parameterized MPC can serve as a structured function approximator, with its parameters learned using RL. The approach is illustrated on a point-mass racing task with future reference information.

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

Robotics increasingly relies on GPUs for parallel simulation, large-scale learning, and neural-network inference. For model predictive control (MPC) to scale with this paradigm, solvers must run efficiently on this hardware while remaining fast, differentiable, and compatible with expressive MPC formulations used in robotics. We present TurboMPC, a differentiable MPC solver that runs entirely on the GPU and supports state and control inequality constraints, implicit integrators, cross-time-coupled costs, and slack variables. TurboMPC combines sequential quadratic programming (SQP), an alternating direction method of multipliers (ADMM) inner solver, implicit differentiation, and a co-designed JAX-CUDA implementation for efficiency and ease of use. In simulation, we validate TurboMPC on constrained planning, humanoid imitation learning, and reinforcement learning with neural-network cost function tasks, achieving up to $15\times$ and $58\times$ speedups over state-of-the-art CPU and GPU differentiable solvers, respectively. We deploy TurboMPC on a full-scale car for minimum-time racing and find that batched, GPU-accelerated tuning of MPC parameters via Bayesian optimization yields significantly faster driving than a hand-tuned baseline. TurboMPC also scales to planning horizons of over $8000$ knot points while maintaining control of the vehicle. We open-source TurboMPC at: https://github.com/ToyotaResearchInstitute/turbompc

Efficient sorter diversion control of automated material handling systems (MHS) is critical for optimizing operational efficiency in large-scale warehouse environments. In this study, we use an inbound receiving sorter at a high-volume e-commerce warehouse as our primary use case, where the sorter diversion system relies on cost functions with static weight configurations that fail to adapt to highly dynamic system contexts, such as volume mode, congestion level, equipment physical status, and upstream/downstream dependencies. To address this real-time sorter diversion optimization challenge, we conducted a comparative study of three candidate hybrid machine learning frameworks: Linear Regression with Gradient Descent Optimization (LR+GDO), XGBoost with Bayesian Optimization (XGB+BO), and Bayesian Contextual Bandits (BCB). Model training and evaluation were enabled by leveraging a high-fidelity physics-aware emulator to overcome the cold-start problem and allow a safe transition from offline to online learning. We performed comprehensive evaluations including reward model predictive accuracy, contextual sensitivity, action distribution, and projected reward uplift. Our results demonstrate that while tree-based reward models offer slightly better predictive power, the BCB framework achieved overall higher performance with 2.03% reward uplift over the heuristic baseline. Furthermore, BCB exhibits several superior characteristics, such as its decisive time-optimal policy backed by Bang-Bang control theory, continuous online learning capability, strategic balance between exploration and exploitation, and significantly shorter inference latency. These results demonstrate the potential of the BCB framework for real-time control optimization in large-scale warehouse environments, motivating further investigation toward operational deployment.

At the core of most socio-technical systems lies a scarce resource that is allocated among agents: highway lanes, public transit, road space, water rights, energy access, grid capacity, user attention, pollution rights, etc. With further automation of the underlying allocation processes, control engineers are increasingly tasked to make decisive assumptions regarding what society wants. In practice to date, design choices are largely driven by industry norms and conventions rather than a result of conscientiously responsible and ethical design. In this paper, we look at tools available to control engineers to design systems in a more principled manner in order to match the societal mandate. We consider three control design paradigms: online feedback optimization, control of Markov decision processes, and model predictive control. Beginning with aggregating individual agents' preferences into control design objectives, subsequently ensuring and certifying the fulfillment of those specifications, we argue that the feedback nature of control systems enables appropriate allocation of the shared resources in ways hitherto unparalleled.

This paper addresses the problem of robust formation control by introducing Topological Online Learning for Displacement-based (TOLD) formation control, a real-time edge-level adaptation framework. Unlike conventional node-level robust controllers that regulate individual robot inputs without modifying the interaction topology, TOLD updates the interaction topology weights online to directly minimize formation distortion. Two strategies are proposed under the TOLD formation control framework: Online Gradient Flow (OGF) with unconstrained weights and Online Exponential Gradient Flow (OExpGF) with non-negative convex weights. Theoretical analysis establishes that, for single-integrator agents over directed graphs, OExpGF guarantees asymptotic consensus, while OGF ensures bounded formation distortion. Simulations with twelve robots under intermittent disturbances show 1.2%-33.14% median cumulative Root Mean Distortion Error reduction when augmenting TOLD with node-level controllers. Hardware experiments with Crazyflie 2.0 quadrotors demonstrate over 62% (OGF) and 31.4% (OExpGF) reduction in median formation distortion compared to fixed-weight consensus.

A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross index sets, with gradients and Hessians contributing additional linear equations per sample and substantially reducing sample complexity compared to value-only regression. Feedback laws are recovered analytically from the learned value function. In high dimensions, a partial Hessian strategy controls the cost of data generation. The approach is validated on problems of increasing state dimension, where second-order data augmentation is shown to improve approximation accuracy and closed-loop performance, with up to an order-of-magnitude reduction in the number of training samples required relative to lower-order methods.

Dynamic feedback linearization (DFL) is a classical technique for trajectory tracking of unicycle-type mobile robots, but the resulting DFL-based controller becomes singular when the linear velocity vanishes, rendering standard DFL-based controllers unsuitable for stop-and-reverse maneuvers. This paper proposes a quadratic-program (QP)-based optimal control framework that avoids this singularity, while establishing local Lipschitz continuity of the resulting feedback law. Our approach reformulates the DFL constraints as an equality-constrained QP with a slack variable, ensuring feasibility for all states and reference signals, including at points where the robot's velocity vanishes. By introducing slack variables and tunable parameters, we demonstrate that the singular configuration can be avoided for a large class of reference trajectories. The effectiveness of the proposed approach for trajectory tracking is demonstrated through ROS 2-Gazebo simulations on a TurtleBot3 Waffle robot. The code is available at https://gradslab.github.io/DFL_QP_Unicycle/

Neural world models coupled with model predictive control (MPC) replan at every environment step to bound accumulated prediction error, but this incurs substantial computational overhead. Reusing a cached plan reduces this overhead, yet its effectiveness depends on how prediction mismatch propagates through the local dynamics. We analyze this trade-off with a perturbation-based dynamic-regret framework and show that stale-plan penalties scale with the reuse tolerance, the accumulated mismatch since the last replanning step, and the local dynamics sensitivity. Based on this structure, we propose AdaReP, a training-free wrapper that adapts the replanning tolerance online using the current deviation from the cached rollout and a local sensitivity estimate, without modifying the learned world model or planner. Across image-space planning, latent-space control, and real-world robotic manipulation, AdaReP substantially reduces planner-side computation while maintaining comparable task performance, including over 80% fewer queries on a 50-trial physical robot study.

Many recent vision-language-action (VLA) policies adopt an imagine-then-act design. A world-action model (WAM) first imagines a short future as a latent trajectory z~, on which the action is then conditioned. We identify this trusted imagination, rather than the reactive policy, as the exposed attack surface. A downstream oracle, such as a safety gate, a visual model-predictive-control (MPC) planner, or an imagine-then-check verifier, consumes z~ as a prediction of the future. The robustness of the policy therefore does not entail the robustness of systems that rely on the WAM. The underlying phenomenon is an asymmetry. Corrupting the imagination is easy, since it requires only displacing z~ from its natural-future manifold. Steering it precisely is hard, since it must reach a specified on-manifold target. We adopt a capability-based threat model with an L-infinity-bounded observation perturbation. The attacker applies projected gradient descent through the fully differentiable observation-to-imagination map. The same off-manifold property motivates a parameter-free denoiser detector. We evaluate three targets: RynnVLA-002, LingBot-VA, and LaDi-WM. Untargeted corruption is roughly 60x stronger than random and is detected at AUC 1.0. Targeted control remains bounded. An adaptive attacker evades detection only by forgoing corruption. The reactive policy remains robust to corrupted imagination. A native imagination-driven MPC, however, exhibits the first adversary-specific task failure (at epsilon=0.01, success 0.70 versus 0.05; Fisher p < 10^-4).

Diffusion policies have recently emerged as a powerful paradigm for representing complex action distributions in reinforcement learning (RL). However, their application to online RL remains limited by the challenge of scalable training in the absence of ground-truth data, where standard optimization techniques such as score matching are not directly applicable. In this work, we introduce a highly efficient algorithm for optimizing diffusion policies by leveraging recent advances in stochastic optimal control. Our approach is based on adjoint matching, which enables simulation-free training and circumvents the need for explicit likelihood estimation or costly backpropagation through the diffusion process. Furthermore, we propose several extensions that improve the robustness and stability of the method in practical settings. Empirical results demonstrate that our approach achieves competitive performance while significantly reducing computational overhead, making diffusion policies more viable for online RL scenarios.

Hybrid neural networks (HNNs) that integrate artificial neural networks (ANNs) with brain-inspired neural networks have achieved broad success across perception and control tasks. However, much of the current success is confined to neuron-scale hybridization, where discrete, spike-based coding fundamentally limits applicability to continuous-state estimation tasks. In neuroscience, continuous attractor neural networks (CANNs) represent continuous states through neural ensembles, pointing to a population-scale route for HNNs to address this limitation. Yet, principled methodologies for ANN-CANN integration remain largely underexplored. In this work, we propose a theory-grounded ANN-CANN hybridization framework and instantiate it as a hybrid tracking neural network (HTNN) for visual object tracking, a representative continuous-state estimation task. The framework aligns ANN response maps with CANN dynamics in the same state space, enabling the two heterogeneous branches to interact through the shared state representation. Furthermore, we uncover a functional bias-variance complementarity: data-driven ANNs provide asymptotically unbiased estimates, while CANN estimates are low-variance but temporally lagged. By operationalizing this complementarity, HTNN achieves stable and accurate tracking across nine visual tracking benchmarks, consistently outperforming single-network baselines and existing hybrid models. Notably, these performance gains are robustly maintained even under diverse environmental variations, including occlusion, motion blur, and background interference. Through this proof-of-concept study, our framework offers a generalizable foundation for advancing HNNs toward population-scale hybridization.

Physical neural networks promise low-power machine learning by computing directly with analogue device physics, but most architectures force nonlinear device responses to act as scalar weights. Inspired by Kolmogorov-Arnold networks, we place trainable nonlinear functions on the connections, making each physical connection a learnable computational element. Realising these functions as analogue band-pass filters on field-programmable analogue arrays, we find that the benefit is task-dependent and follows from the smoothness of the physical basis: the networks represent smooth, continuously valued targets, including robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking, with far fewer nodes and connections than multilayer perceptrons, but offer no parameter-efficiency advantage on classification-like decision boundaries. Trained networks transfer to hardware across approximately 35,000 connections with quantified fidelity, and a dedicated CMOS implementation is projected to operate at approximately 30 microwatts. A memristive realisation reproduces the same behaviour in simulation, indicating that the advantage comes from placing trainable nonlinearity on connections, rather than from a particular device.

An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators with an arbitrary number of links, formulated entirely within the Lie group SE(3). The group-affine property of the kinematic equations makes the linearised error dynamics autonomous, so the Riccati equation governs the true error covariance rather than a local approximation. A physically separated noise model treats gyroscope and accelerometer channels independently: the accelerometer provides translational twist via gravity-compensated integration, yielding a measurement covariance that scales with the sample interval in exact analogy with process noise discretisation; a state-dependent Coriolis noise term captures gyroscope noise propagating through the nonlinear dynamics, vanishing at rest and growing with twist magnitude. The filter is structured as a modular chain of per-link IEKFs in which the predicted covariance of each link depends on its predecessor only through the Adjoint-transformed posterior, giving linear computational cost in link count. Exponential ultimate boundedness in mean square is established via a Lie algebra Lyapunov function, with per-link bounds chained through the Adjoint operator norm to yield a stability certificate that is modular and scalable to arbitrary chain length. Numerical results validate the design.