Model Predictive Control

We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of existing operator learning methods, many of which are primarily tailored for continuous-time problems, while a large class of system-identification problems is intrinsically discrete-time. The $z$-domain form expresses stability as a unit-disk pole constraint and makes learned discrete-time poles directly readable. The model combines low-rank channel mixing, smooth stable pole reparameterization, causal recurrence, and an optional short finite impulse response (FIR) branch in a single $z$-domain rational recurrent layer. Across controlled discrete system-identification experiments, ZNO's advantage is most evident when the target dynamics are stable rational systems with lightly damped poles near the unit circle. Under matched parameter budgets, ZNO is not uniformly dominant; however, with validation-selected configurations, the same architecture can achieve the lowest mean error across the controlled tasks. A five-bin difficulty sweep over near-unit-circle / long-memory dynamics shows that ZNO has the lowest mean error across memory regimes, from short (approximately 10 steps) to long (approximately 100-200 steps). On five public nonlinear system-identification benchmarks, ZNO is competitive with neural operator and state-space baselines, achieving the lowest mean error on benchmarks whose dynamics align with stable rational discrete-time filters, while classical or state-space baselines remain preferable on some systems. These results position ZNO as a strong model for stable rational discrete-time dynamics, especially in near-unit-circle and long-memory regimes, but not as a universal replacement for specialized system-identification methods.

Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods derive from information-theoretic objectives that are agnostic to the geometry of the control problem, leading to pathological behaviors such as mode-averaging when the cost landscape is complex. We present OT-MPC, a sampling-based algorithm that overcomes these limitations through an entropy-regularized optimal transport formulation. By computing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC refines candidates toward nearby promising samples while coordinating updates across the ensemble to maintain coverage of the solution space. We derive closed-form, gradient-free updates via the Sinkhorn algorithm, enabling real-time performance. Experiments on navigation, manipulation, and locomotion tasks demonstrate improved success rates over existing methods.

Autonomous spacecraft docking requires control policies that simultaneously ensure collision avoidance and target reachability under coupled, high-dimensional translational-rotational dynamics. Hamilton-Jacobi (HJ) reachability provides formal reach-avoid guarantees, but classical solvers are limited to low-dimensional systems. Learning-based approaches have begun to scale HJ analysis, yet they struggle in reach-avoid settings, especially where goal and failure sets are tightly coupled, as in docking. We propose a learning-based Backward Reach-Avoid Tube (BRAT) framework that addresses this challenge by tightly integrating HJ structure with MPC-based supervision. In the offline phase, we train a neural approximation of the HJ value function using PDE-based losses augmented with curriculum-driven MPC supervision, which provides informative value targets and stabilizes training in regions where purely PDE-based methods fail. In the online phase, the learned value function is deployed through two real-time controllers: (i) a value gradient-driven controller, and (ii) a value-function-augmented terminal MPC that explicitly enforces reachability at the horizon. We evaluate the proposed method on a 6D planar docking problem against grid-based ground truth and then scale to the full 13D system. Across both settings, our approach outperforms existing methods in success rate and computational efficiency.

Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control theoretic ideas with reinforcement learning through control guided learning. A notable example of this is the use of a control Lyapunov function (CLF) to synthesize the reinforcement learning rewards, a technique known as CLF-RL, which has shown practical success. This paper investigates the stability properties of optimal controllers using CLF-RL with the goal of bridging experimentally observed stability with theoretical guarantees. The RL problem is viewed as an optimal control problem and exponential stability is proven in both continuous and discrete time using both core CLF reward terms and the additional terms used in practice. The theoretical bounds are numerically verified on systems such as the double integrator and cart-pole. Finally, the CLF guided rewards are implemented for a walking humanoid robot to generate stable periodic orbits.

This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge from observations, and the optimal course of action depends on these observations. \revise{Trajectory-trees, optimized in belief space, naturally capture this dependency by branching where the belief state is expected to evolve into multiple distinct scenarios, such as upon receiving an observation. Unlike sequential trajectories, which model a single forward evolution of the system, trajectory-trees capture multiple possible contingencies.} First, we focus on Model Predictive Control (MPC) and demonstrate the benefits of planning tree-like trajectories. We formulate the control problem as the optimization of a tree with a single branching (PO-MPC). This improves performance by reducing control costs through more informed planning. To satisfy the real-time constraints of MPC, we develop an optimization algorithm called Distributed Augmented Lagrangian (D-AuLa), which leverages the decomposability of the PO-MPC formulation to parallelize and accelerate the optimization. We apply the method to both linear and non-linear MPC problems using autonomous driving examples. Second, we address Task And Motion Planning (TAMP), and introduce a planner (PO-LGP) reasoning on decision trees at task level, and trajectory-trees at motion-planning level. This approach builds upon the Logic-Geometric-Programming Framework (LGP) and extends it to partially observable problems. The experiments show the method's applicability to problems with a small belief state size, and scales to larger problems by optimizing explorative policies, which are used as macro-actions in an overarching task plan.

Autonomous navigation and obstacle avoidance remain a core challenge of modern Unmanned Aerial Vehicles (UAVs). While traditional control methods struggle with the complexity and variability of the environment, reinforcement learning (RL) enables UAVs to learn adaptive behaviors through interaction with the environment. Existing research with RL prioritizes the mission success at the expense of mission time and safety of UAVs. This study integrates Potential Based Reward Shaping (PBRS) with Control Lyapunov Functions (CLF) and Control Barrier Functions (CBF) to simultaneously optimize mission time and ensure formal safety guarantees. An RL model is trained in a generalized simple environment, then used in complex scenarios incorporating a CLF-CBF-QP filter without further training. Experimental results in simulated environments demonstrate a significant reduction in mission time and outstanding performance in complex environment.

Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schrödinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network. In contrast, we identify a restricted but sufficiently broad and analytically solvable class in which the score, intermediate marginals, and protocol gradients are available in closed form without inner stochastic simulation loops and without neural networks in the optimization loop. We recast the classical linear--quadratic--Gaussian (LQG) stochastic-control structure as a transport problem of the Path Integral Diffusion (PID) type. In classical LQG control, linear dynamics, Gaussian noise, and quadratic costs lead to Riccati equations and closed-form optimal feedback. In LQ-GM-PID, we retain the linear--quadratic stochastic-control backbone, but replace terminal state regulation by a prescribed terminal probability density and allow both the initial and terminal laws to be Gaussian Mixtures (GM). Moreover, LQ-GM-PID turns bridge diffusion from a tool for terminal target matching alone into a tool for path shaping. We demonstrate this on a 2D corridor task, a 2D multi-entrance transport task, and a high-dimensional scaling study with $d=32$ and $M=16$ Gaussian-mixture terminal modes, all with sub-50,ms analytic precompute on a laptop. We position LQ-GM-PID as an analytically solvable reference model for the state-of-the-art neural bridge-diffusion and generative-transport methods: a controlled setting in which neural approximations, score estimates, path-shaping objectives, and protocol-learning procedures can be tested against exact quantities.

We study homogeneous refinement operators $(Vγ)(t)=\sum_{j\in\mathbb Z}A_jγ(Mt-j)$, acting on compactly supported continuous piecewise linear curves $γ:\mathbb R\to\mathbb R^p$, where $M\ge2$ and only finitely many matrices $A_j\in\mathbb R^{p\times p}$ are nonzero. We prove that the iterates $V^nγ$ admit exact ReLU realizations of fixed width and depth $O(n)$. The main new ingredient is an exact loop controller for the residual dynamics. Instead of propagating scalar residual surrogates, the construction transports the residual orbit by a forward-exact state on a polygonal loop. Scalar factors and digit selectors are then recovered from this loop state by complementary CPwL readouts. The loop seam is not removed, but its remaining ambiguity is confined to the final readout/selector stage, where it is harmless because the scalar atom is supported away from the seam. This gives a homogeneous $M$-ary vector-valued extension of the scalar binary refinable-function construction with a more geometric controller architecture. We also record crude exponential bounds on the network weights and biases. Affine forcing terms are handled by expanding affine iterates into finite sums of homogeneous iterates, giving exact fixed-width realizations with depth $O(n^2)$, and anchored open curves reduce to compactly supported defects with affine anchor mismatch. We also describe homogeneous polygonal generators, including dragon-type examples and a self-intersecting Hilbert-type prototype in arbitrary dimension. The extended version includes stage-dependent forcing, finite-state stacking reductions, and further geometric constructions such as Koch-, Gosper-, Morton-, and connector-based Hilbert-type variants.

In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach transforms the nonlinear PDEs describing the Cosserat rod to a system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on state-feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.

We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward fine-tuning of pre-trained models. This problem can be approached from a stochastic optimal control (SOC) perspective, using adjoint-based or score matching methods, or from a non-equilibrium thermodynamics perspective. We provide a unified framework encompassing these approaches and make three main contributions: (i) bias-variance decompositions revealing that Adjoint Matching/Sampling and Novel Score Matching have finite gradient variance, while Target and Conditional Score Matching do not; (ii) norm bounds on the lean adjoint ODE that theoretically support the effectiveness of adjoint-based methods; and (iii) adaptations of the CMCD and NETS loss functions, along with novel Crooks and Jarzynski identities, to the exponential tilting setting. We validate our analysis with reward fine-tuning experiments on Stable Diffusion 1.5 and 3.

Policy optimization in high-dimensional continuous control for robotics remains a challenging problem. Predominant methods are inherently local and often require extensive tuning and carefully chosen initial guesses for good performance, whereas more global and less initialization-sensitive search methods typically incur high rollout costs. We propose TFM-S3, a tabular hybrid local-global method for improving global exploration in robot policy learning with limited rollout cost. We interleave high-frequency local updates with intermittent rounds of global search. In each search round, we construct a dynamically updated low-dimensional policy subspace via SVD and perform iterative surrogate-guided refinement within this space. A pretrained tabular foundation model predicts candidate returns from a small context set, enabling large-scale screening with limited rollout cost. Experiments on continuous control benchmarks show that TFM-S3 consistently accelerates early-stage convergence and improves final performance compared to TD3 and population-based baselines under an identical rollout budget. These results demonstrate that foundation models are a powerful new tool for creating sample-efficient policy learning methods for continuous control in robotics.

Dense, dynamic crowds pose a persistent challenge for autonomous mobile robots. Purely reactive planning methods, such as Model Predictive Path Integral (MPPI) control, often fail to escape local minima in complex scenarios due to their limited prediction horizon. To bridge this gap, we propose Ray-based Task-Oriented Latent Dynamics (RAY-TOLD), a hybrid control architecture that integrates obstacle information into latent dynamics and utilizes the robustness of physics-based MPPI with the long-horizon foresight of reinforcement learning. RAY-TOLD leverages a LiDAR-centric latent dynamics model to encode high-dimensional sensor data into a compact state representation, enabling the learning of a terminal value function and a policy prior. We introduce a policy mixture sampling strategy that augments the MPPI candidate population with trajectories derived from the learned policy, effectively guiding the planner towards the goal while maintaining kinematic feasibility. Extensive tests in a stochastic environment with high-density dynamic obstacles demonstrate that our method outperforms the MPPI baseline, reducing the collision rate. The results confirm that blending short-horizon physics-based rollouts with learned long-horizon intent significantly enhances navigation reliability and safety.

This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in the single agent's model. We first show that, under discretely sampled actions, the value function in the exploratory formulation converges to the one in the relaxed control formulation as the time grid refines. Leveraging the relaxed control formulation, we derive the exploratory Hamilton-Jacobi-Bellman (HJB) equation, in which the controlled common noise gives rise to an additional nonlinear functional of policy, rendering the policy iteration intricate. Under certain concavity condition, we establish the existence and uniqueness of the optimal one-step policy iteration via a first-order condition using the partial linear functional derivative with respect to policy. The policy improvement at each iteration is verified by relating to an entropy-regularized optimization problem over the space of policies. In the mean-field setting, we introduce the integrated q-function (Iq-function) defined on the state distribution and the policy, and it is shown that an optimal policy is identified as a two-layer fixed point to the argmax operator of the Iq-function. Finally, we provide the explicit characterization of an optimal policy as a Gaussian distribution in the general linear-quadratic (LQ) setting.

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as \textit{guidance}. Despite their widespread use, existing guidance methods either require expensive multi-particle, many-step schemes or rely on poorly understood approximations. We reformulate guidance as a \textit{deterministic optimal control problem}, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the \textit{flow map}, an object of significant recent interest for its role in fast inference, arises naturally in the optimal solution. Based on this observation, we propose \textbf{Flow Map Reward Guidance (FMRG)}: a training-free, \textit{single-trajectory} framework that uses the flow map to both integrate and guide the flow. At text-to-image scale, FMRG matches or surpasses baselines across inverse problems and reward-guided generation with \textbf{as few as 3 NFEs}, giving at least an order-of-magnitude speedup in comparison to prior state of the art. Code is available at https://github.com/jrrhuang/fmrg.

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such as Model Predictive Control (MPC), where one repeatedly solves related optimization problems with fixed structure and changing parameter values, we propose learning online updates of the relaxation parameter to improve performance on problem classes of interest. This choice is computationally attractive in OSQP-like architectures, since adapting relaxation does not trigger the matrix refactorizations associated with penalty updates. We establish convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions, and show on benchmark quadratic programs that the resulting learned policies improve both iteration count and wall-clock time over baseline OSQP.

Safe navigation in cluttered environments is an important challenge for autonomous systems. Robots navigating through obstacle ridden scenarios need to be able to navigate safely in the presence of obstacles, goals, and ego objects of varying geometries. In this work, reachable set representations of the robot's real-time capabilities in the state space can be utilized to capture safe navigation requirements. While neural radiance fields (NeRFs) are utilized to compute, store, and manipulate the volumetric representations of the obstacles, or ego vehicle, as needed. Constrained optimal control is employed to represent the resulting path planning problem, involving linear matrix inequality constraints. We present simulation results for path planning in the presence of numerous obstacles in two different scenarios. Safe navigation is demonstrated through using reachable sets in the corresponding constrained optimal control problems.

Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability. Meanwhile, model-based RL (MBRL) methods routinely employ probabilistic ensemble (PE) neural networks to capture complex, high-dimensional dynamics from data with minimal prior knowledge. However, existing attempts to integrate PEs into PSFs lack rigorous uncertainty quantification. We introduce the Uncertainty-Aware Predictive Safety Filter (UPSi), a PSF that provides rigorous safety predictions using PE dynamics models by formulating future outcomes as reachable sets. UPSi introduces an explicit certainty constraint that prevents model exploitation and integrates seamlessly into common MBRL frameworks. We evaluate UPSi within Dyna-style MBRL on standard safe RL benchmarks and report substantial improvements in exploration safety over prior neural network PSFs while maintaining performance on par with standard MBRL. UPSi bridges the gap between the scalability and generality of modern MBRL and the safety guarantees of predictive safety filters.

We present a Spatially Embedded Evolutionary Algorithm where robot individuals exist in a physically simulated 2D environment, must navigate to encounter potential mates, and compete for survival under various spatially-aware selection pressures. Using HyperNEAT evolved neural controllers for ARIEL gecko-inspired quadrupeds in MuJoCo, we investigate how spatial structure fundamentally alters evolutionary dynamics. Our experiments show a modest 4.9% difference in peak fitness between proximity-based and random pairing possibly within stochastic variation while combining spatial parent selection with stochastic death selection produces unstable population dynamics. We discover a continuous phase transition in energy-based selection experiments, with critical zone count separating extinction-dominated and explosion-dominated regimes. Our density-dependent death selection mechanism achieves 97% completion rates but causes fitness decline, revealing a fundamental dilemma where decoupled mechanisms produce bistable dynamics, positively coupled mechanisms create counter-selection pressures, and only deterministic fitness-based selection maintains stability. These findings provide important constraints for future spatial EA design.

Probing frozen vision transformers typically uses permutation-invariant aggregation (GAP or $\texttt{[CLS]}$), treating patch tokens as an unstructured set. Content-dependent probes such as self-attention are useful accuracy controls, but they do not expose a fixed token schedule or fixed position weights for auditing. We introduce $\textbf{SSMProbe}$, an explicitly inspectable probe that replaces invariant pooling with a Sinkhorn-learned evidence route followed by a diagonal S4 decoder. The S4 decoder is a linear time-invariant (LTI) system whose final state has fixed, position-dependent coefficients, so the probe-induced routed sequence can be audited as a concrete object rather than inferred only from accuracy. Our central measurement is the geometry of routed evidence: which patch tokens are moved to influential positions by this diagnostic, whether those tokens form spatially organized regions or random-like dispersed sets, and how the fixed S4 kernel weights them. Across MAE, BEiT, DINOv2, and supervised ViT, this route geometry separates MAE's dispersed, nearly random-like routes from the more spatially organized routes of BEiT, ViT, and DINOv2, with DINOv2 retaining a distinct strong $\texttt{[CLS]}$ profile. SSMProbe uses the mathematical transparency of state-space models to turn a frozen ViT readout into an auditable evidence-routing analysis.

Offline reinforcement learning (RL) agents often fail when deployed, as the gap between training datasets and real environments leads to unsafe behavior. To address this, we present SAS (Self-Alignment for Safety), a transformer-based framework that enables test-time adaptation in offline safe RL without retraining. In SAS, the main mechanism is self-alignment: at test time, the pretrained agent generates several imagined trajectories and selects those satisfying the Lyapunov condition. These feasible segments are then recycled as in-context prompts, allowing the agent to realign its behavior toward safety while avoiding parameter updates. In effect, SAS turns Lyapunov-guided imagination into control-invariant prompts, and its transformer architecture admits a hierarchical RL interpretation where prompting functions as Bayesian inference over latent skills. Across Safety Gymnasium and MuJoCo benchmarks, SAS consistently reduces cost and failure while maintaining or improving return.

We study gradient descent for rank-1 matrix factorization through a state-dependent Lyapunov perspective. The central object is a parameterized quadratic certificate $I(δ;\,\cdot)$ whose boundary-inward property induces a monotone state parameter $δ_t$, thereby certifying that the trajectory is confined to a shrinking family of level sets. For certified initializations below the critical step size, this mechanism proves convergence to global minimizers. Above the critical step size, the same monotone-state mechanism instead leads to a balanced terminal regime; for a range of post-critical step sizes, the reduced dynamics exhibit period-2 behavior consistent with edge-of-stability phenomena. We further show that the scalar certificate is not an ad hoc algebraic construction: under structural axioms and a natural state-parameter normalization, it is uniquely determined by the monotonicity mechanism. Numerical experiments suggest that this state-dependent Lyapunov mechanism persists beyond the proved cases, including two-dimensional rank-1 approximation and quartic augmentations of scalar factorization.

Contact variability, sensing uncertainty, and external disturbances make grasp execution stochastic. Expected-quality objectives ignore tail outcomes and often select grasps that fail under adverse contact realizations. Risk-sensitive POMDPs address this failure mode, but many use particle-filter beliefs that scale poorly, obstruct gradient-based optimization, and estimate Conditional Value-at-Risk (CVaR) with high-variance approximations. We instead formulate grasp acquisition as variational inference over latent contact parameters and object pose, representing the belief with a differentiable Gaussian mixture. We use Gumbel-Softmax component selection and location-scale reparameterization to express samples as smooth functions of the belief parameters, enabling pathwise gradients through a differentiable CVaR surrogate for direct optimization of tail robustness. In simulation, our variational neural belief improves robust grasp success under contact-parameter uncertainty and exogenous force perturbations while reducing planning time by roughly an order of magnitude relative to particle-filter model-predictive control. On a serial-chain robot arm with a multifingered hand, we validate grasp-and-lift success under object-pose uncertainty against a Gaussian baseline. Both methods succeed on the tested perturbations, but our controller terminates in fewer steps and less wall-clock time while achieving a higher tactile grasp-quality proxy. Our learned belief also calibrates risk more accurately, keeping mean absolute calibration error below 0.14 across tested simulation regimes, compared with 0.58 for a Cross-Entropy Method planner.

This paper presents a sensitivity-based tube Nonlinear Model Predictive Control (NMPC) framework for cooperative aerial chains under bounded parametric uncertainty. We consider a planar two-vehicle chain connected by rigid links, modeled with input-rate actuation to enforce slew-rate and magnitude limits on thrust and torque. Robustness to uncertainty in link mass, length, and inertia is achieved by propagating first-order parametric state sensitivities along the horizon and using them to compute online constraint-tightening margins. We robustify an inter-link separation constraint, implemented via a smooth cosine embedding, and thrust-magnitude bounds. The method is implemented in MATLAB and evaluated with boundary-hugging maneuvers and Monte-Carlo uncertainty sampling. Results show improved constraint margins under uncertainty with tracking performance comparable to nominal NMPC.

Tendon-Driven Continuum Robots (TDCRs) pose significant modeling and control challenges due to complex nonlinearities, such as frictional hysteresis and transmission compliance. This paper proposes a differentiable learning framework that integrates high-fidelity dynamics modeling with robust neural control. We develop a GRU-based dynamics model featuring bidirectional multi-channel connectivity and residual prediction to effectively suppress compounding errors during long-horizon auto-regressive prediction. By treating this model as a gradient bridge, an end-to-end neural control policy is optimized through backpropagation, allowing it to implicitly internalize compensation for intricate nonlinearities. Experimental validation on a physical three-section TDCR demonstrates that our framework achieves accurate tracking and superior robustness against unseen payloads, outperforming Jacobian-based methods by eliminating self-excited oscillations. For implementation details and source code, please refer to https://github.com/ZiqingZou/ContinuumControl.

While it is generally understood that zeroth-order (ZO) algorithms have an extra dependency on their number of iterations for any choice of parameters, compared to their first-order (FO) counterparts, in this work, we show that under several conditions, in expectation, ZO methods do not suffer from extra dimension dependencies in their convergence rates with respect to their FO counterparts. We look at optimisation algorithms from the dynamical systems perspective and analyse the conditions under which one can formulate the average of a ZO algorithm as the average of its FO counterpart with bounded perturbations with values dependent on design parameters. Then, using input-to-state stability properties, we show ZO methods follow the same decay rate as their FO counterparts and converge to a neighbourhood of the fixed point of FO methods, where its radius depends on the bound of the norm of the perturbations, which can be made arbitrarily small. The theoretical findings are illustrated via numerical examples.

We propose VISION-SLS, a method for nonlinear output-feedback control from high-resolution RGB images which provides robust constraint satisfaction guarantees under calibrated uncertainty bounds despite partial observability, sensor noise, and nonlinear dynamics. To enable scalability while retaining guarantees, we propose: (i) a learned low-dimensional observation map from pretrained visual features with state-dependent error bounds, and (ii) a causal affine time-varying output-feedback policy optimized via System Level Synthesis (SLS). We develop a scalable, novel solver for the resulting nonconvex program that leverages sequential convex programming coupled with efficient Riccati recursions. On two simulated visuomotor tasks (a 4D car and a 10D quadrotor) with >= 512 x 512 pixels and a 59D humanoid task with partial observability, our method enables safe, information-gathering behavior that reduces uncertainty while guaranteeing constraint satisfaction with empirically-calibrated error bounds. We also validate our method on hardware, safely controlling a ground vehicle from onboard images, outperforming baselines in safety rate and solve times. Together, these results show that learned visual abstractions coupled with an efficient solver make SLS-based safe visuomotor output-feedback practical at scale. The code implementation of our method is available at https://github.com/trustworthyrobotics/VISION-SLS.

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.

We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control ($\texttt{B-MPC}$) method that plans directly over both the estimated state and its error covariance. In particular, $\texttt{B-MPC}$ plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that $\texttt{B-MPC}$ can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.

Runtime monitoring of stochastic systems must distinguish nominal distributional relaxation from regime departure while controlling repeated-test false alarms under explicit validity assumptions. This paper links relative-entropy dissipation, information geometry, and sequential inference in a bounded first-passage monitoring architecture. For reversible Fokker--Planck dynamics, relative entropy to an invariant density is non-increasing; under exogenous forcing, its derivative decomposes into nominal dissipation and an information-space forcing term. The runtime layer uses Gaussian window surrogates, nominal-relative covariance shrinkage, a coordinate-consistent relative precision diagnostic, and randomized conformal ranks aggregated by a mixture power-martingale process. Analytical Ornstein--Uhlenbeck validation gives zero positive nominal Kullback--Leibler increments, forcing-identity residuals below 3.31 x 10^-6, and coordinate-invariance errors at numerical roundoff. On NSL-KDD, the monitor yields 0/100 alarms on internal nominal streams but 63/100 on official test-normal streams; post-change detection is 99.0% for seen and 98.53% for test-only attack types with median one-window delay. On UNSW-NB15, internal-null alarms are 0/100, whereas official test-normal alarms rise to 90/100; post-change detection is 81.33%, with 18.67% pre-change alarms. In these evaluations, calibration transport emerges as a major deployment constraint. No universal benchmark superiority, causal inference, or physical-work interpretation is claimed.

This paper presents a trajectory planning method for articulated commercial vehicles, specifically tractor-semitrailers, based on Model Predictive Contouring Control (MPCC). Although MPCC has proven effective for passenger cars, it is generally ill-suited for tractor-semitrailers. These vehicles are significantly larger, the semitrailer follows a different path than the tractor, and reversing maneuvers are unstable and prone to jackknifing. Furthermore, practical driving scenarios often require scenario-dependent prioritization of different vehicle `anchor points', e.g., prioritizing the semitrailer position during docking or the tractor position when parking to charge. Therefore, we extend MPCC to enable scenario-dependent weighting of these anchor points and incorporate explicit road-boundary constraints for the front and rear tractor axles and the semitrailer axle, thereby ensuring that all considered wheels remain within the drivable area. The simulation results demonstrate the successful navigation of a representative logistic scenario in both forward and reverse direction. Furthermore, the influence of the optimization parameters on the trajectories is analyzed, providing insights into controlling the vehicle behavior. Finally, first tests using a full-scale prototype vehicle show the practical applicability of the approach.

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.

Ensuring safe exploration in high-dimensional systems with unknown dynamics remains a significant challenge. Existing safe reinforcement learning methods often provide safety guarantees only in expectation, which can still lead to safety violations. Control-theoretic approaches, in contrast, offer hard constraint-based safety guarantees but typically assume access to known system dynamics or require accurate estimation of control-affine models. In this paper, we propose a safe reinforcement learning framework that learns a probabilistic control-affine dynamics model in an offline setting. The learned model is leveraged to explicitly construct control barrier functions (CBFs) that incorporate model uncertainty to provide conservative safety constraints. These CBF constraints are enforced through an online constraint-based action correction mechanism, enabling safe exploration without overly restricting task performance. Empirical evaluations on nonlinear, complex continuous-control benchmarks demonstrate that our approach achieves returns comparable to those of existing baselines while significantly reducing safety violations.

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.

Iterative self-correction is increasingly deployed in agentic LLM systems, yet whether repeated refinement improves or degrades performance remains inconsistent across models. We recast self-correction as a closed-loop feedback-control problem in which the same model is both controller and plant, and analyze its error dynamics via a two-state Markov model over {Correct, Incorrect}, parameterized by the Error Introduction Rate (EIR) and Error Correction Rate (ECR). The model yields a directly measurable stability threshold -- iterate only when ECR/EIR > Acc/(1-Acc) -- in which EIR acts as a stability margin and prompting becomes lightweight controller design. Empirically, across 7 models and 3 datasets (GSM8K, MATH, StrategyQA), a sharp near-zero EIR boundary (< 0.5%) cleanly separates beneficial from harmful self-correction: only o3-mini (+3.4 pp), Claude Opus 4.6 (+0.6 pp), and o4-mini (+/-0 pp) stay non-degrading, while GPT-5 and four others lose accuracy. A verify-first prompt intervention then provides causal evidence: it drives GPT-4o-mini's EIR from 2% to 0% and converts a -6.2 pp degradation into +0.2 pp (paired McNemar, p<10^{-4}), with negligible change on already-sub-threshold models -- exactly as the diagnostic predicts. A complementary analysis of adaptive self-consistency (ASC) shows it halts harmful refinement at a 3.8 pp confidence-elicitation cost, exposing a two-tier capability structure: prompt-level EIR suppression prevents degradation, whereas ECR enhancement -- plausibly training-level -- is required for genuine gains. Self-correction should thus be treated not as a default behavior but as a control decision governed by measurable error dynamics.

Variable impedance model predictive control (MPC) formulations often treat joint stiffness as an instantaneous decision variable. The resulting feasible set strictly contains the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set F_param and the realizable set F_real, and characterize the regime of mismatch via the dimensionless parameter α = ωsT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold α_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as α decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.986). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold α_infeas < α_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection. Augmenting the prediction state with stiffness closes the mismatch by construction.

We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown $\tilde{O}(T^{2/3})$ regret and satisfaction of robust constraints, leaving open the question of whether $\tilde{O}(\sqrt{T})$ regret can be attained in the constrained LQR setting. We contribute to this problem by showing $\tilde{O}(\sqrt{T})$ regret and satisfaction of chance constraints. This type of constraints allow us to handle unbounded noise and also enable analytical techniques not directly applicable to robust constraints. Our proposed algorithm for this problem uses an SDP to select an optimistic policy, and then "scales back" this policy until it is verifiably-safe. Our theoretical analysis establishes regret and constraint guarantees via a key lemma that bounds the system covariance in terms of the chosen policy. This covariance-based analysis is in contrast with the cost-to-go based analysis that is typically used in adaptive LQR.

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

Discrete-event systems and supervisory control theory provide a rigorous framework for specifying correct-by-construction behavior. However, their practical application to swarm robotics remains largely underexplored. In this paper, we investigate a topological recovery method based on discrete-event-systems within a swarm robotics context. We propose a hybrid architecture that combines a high-level discrete event systems supervisor with a low-level continuous controller, allowing lost drones to safely recover from fault or attack events and re-enter a controlled region. The method is demonstrated using ten simulated UAVs in the py-bullet-drones framework. We show recovery performance across four distinct scenarios, each with varying initial state estimates. Additionally, we introduce a secondary recovery supervisor that manages the regrouping process for a drone after it has re-entered the operational region.

Simultaneous localization and mapping (SLAM) is a foundational state estimation problem in robotics in which a robot accurately constructs a map of its environment while also localizing itself within this construction. We study the active SLAM problem through the lens of optimal stochastic control, thereby recasting it as a decision-making problem under partial information. After reviewing several commonly studied models, we present a general stochastic control formulation of active SLAM together with a rigorous treatment of motion, sensing, and map representation. We introduce a new exploration stage cost that encodes the geometry of the state when evaluating information-gathering actions. This formulation, constructed as a nonstandard partially observable Markov decision process (POMDP), is then analyzed to derive rigorously justified approximate solutions that are near-optimal. To enable this analysis, the associated regularity conditions are studied under general assumptions that apply to a wide range of robotics applications. For a particular case, we conduct an extensive numerical study in which standard learning algorithms are used to learn near-optimal policies.

There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current state-of-the-art bounds do not accurately capture the statistical complexity of system identification, even in the most fundamental setting of estimating a discrete-time linear dynamical system (LDS) via ordinary least-squares regression (OLS). Specifically, we utilize asymptotic normality to identify classes of problem instances for which current bounds overstate the squared parameter error, in both spectral and Frobenius norm, by a factor of the state-dimension of the system. Informed by this discrepancy, we then sharpen the OLS parameter error bounds via a novel second-order decomposition of the parameter error, where crucially the lower-order term is a matrix-valued martingale that we show correctly captures the CLT scaling. From our analysis we obtain finite-sample bounds for both (i) stable systems and (ii) the many-trajectories setting that match the instance-specific optimal rates up to constant factors in Frobenius norm, and polylogarithmic state-dimension factors in spectral norm.

Landing UAVs on heaving marine platforms is challenging because relative vertical motion can generate large impact forces and cause rebound on touchdown. To address this, we develop an impact-aware Model Predictive Control (MPC) framework that models landing as a velocity-level rigid-body impact governed by Newton's restitution law. We embed this as a linear complementarity problem (LCP) within the MPC dynamics to predict the discontinuous post-impact velocity and suppress rebound. In simulation, restitution-aware prediction reduces pre-impact relative velocity and improves landing robustness. Experiments on a heaving-deck testbed show an 86.2% reduction in post-impact deflection compared to a tracking MPC.

The integration of Model Predictive Control (MPC) and Reinforcement Learning (RL) has emerged as a promising paradigm for constrained decision-making and adaptive control. MPC offers structured optimization, explicit constraint handling, and established stability tools, whereas RL provides data-driven adaptation and performance improvement in the presence of uncertainty and model mismatch. Despite the rapid growth of research on RL--MPC integration, the literature remains fragmented, particularly for control architectures built on linear or linearized predictive models. This paper presents a comprehensive Systematic Literature Review (SLR) of RL--MPC integrations for linear and linearized systems, covering peer-reviewed and formally indexed studies published until 2025. The reviewed studies are organized through a multi-dimensional taxonomy covering RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains. In addition, a cross-dimensional synthesis is conducted to identify recurring design patterns and reported associations among these dimensions within the reviewed corpus. The review highlights methodological trends, commonly adopted integration strategies, and recurring practical challenges, including computational burden, sample efficiency, robustness, and closed-loop guarantees. The resulting synthesis provides a structured reference for researchers and practitioners seeking to design or analyze RL--MPC architectures based on linear or linearized predictive control formulations.

Shared Control methods often use impedance control to track target poses in a robotic manipulator. The guidance behavior of such controllers is shaped by the used stiffness gains, which can be varying over time to achieve an adaptive guiding. When multiple target poses are tracked at the same time with varying importance, the corresponding output wrenches have to be arbitrated with weightings changing over time. In this work, we study the stabilization of both variable stiffness in impedance control as well as the arbitration of different controllers through a scaled addition of their output wrenches, reformulating both into a holistic framework. We identify passivity violations in the closed loop system and provide methods to passivate the system. The resulting approach can be used to stabilize standard impedance controllers, allowing for the development of novel and flexible shared control methods. We do not constrain the design of stiffness matrices or arbitration factors; both can be matrix-valued including off-diagonal elements and change arbitrarily over time. The proposed methods are furthermore validated in simulation as well as in real robot experiments on different systems, proving their effectiveness and showcasing different behaviors which can be utilized depending on the requirements of the shared control approach.

Full-batch gradient descent on neural networks drives the largest Hessian eigenvalue to the threshold $2/η$, where $η$ is the learning rate. This phenomenon, the Edge of Stability, has resisted a unified explanation: existing accounts establish self-regulation near the edge but do not explain why the trajectory is forced toward $2/η$ from arbitrary initialization. We introduce the edge coupling, a functional on consecutive iterate pairs whose coefficient is uniquely fixed by the gradient-descent update. Differencing its criticality condition yields a step recurrence with stability boundary $2/η$, and a second-order expansion yields a loss-change formula whose telescoping sum forces curvature toward $2/η$. The two formulas involve different Hessian averages, but the mean value theorem localizes each to the true Hessian at an interior point of the step segment, yielding exact forcing of the Hessian eigenvalue with no gap. Setting both gradients of the edge coupling to zero classifies fixed points and period-two orbits; near a fixed point, the problem reduces to a function of the half-amplitude alone, which determines which directions support period-two orbits and on which side of the critical learning rate they appear.

Training modern neural networks often relies on large learning rates, operating at the edge of stability, where the optimization dynamics exhibit oscillatory and chaotic behavior. Empirically, this regime often yields improved generalization performance, yet the underlying mechanism remains poorly understood. In this work, we represent stochastic optimizers as random dynamical systems, which often converge to a fractal attractor set (rather than a point) with a smaller intrinsic dimension. Building on this connection and inspired by Lyapunov dimension theory, we introduce a novel notion of dimension, coined the `sharpness dimension', and prove a generalization bound based on this dimension. Our results show that generalization in the chaotic regime depends on the complete Hessian spectrum and the structure of its partial determinants, highlighting a complexity that cannot be captured by the trace or spectral norm considered in prior work. Experiments across various MLPs and transformers validate our theory while also providing new insights into the recently observed phenomenon of grokking.

Large Language Models (LLMs) show promise for generating Register-Transfer Level (RTL) code from natural language specifications, but single-shot generation achieves only 60-65% functional correctness on standard benchmarks. Multi-agent approaches such as MAGE reach 95.9% on VerilogEval yet remain untested on harder industrial benchmarks such as NVIDIA's CVDP, lack synthesis awareness, and incur high API costs. We present ChipCraftBrain, a framework combining symbolic-neural reasoning with adaptive multi-agent orchestration for automated RTL generation. Four innovations drive the system: (1) adaptive orchestration over six specialized agents via a PPO policy over a 168-dim state (an alternative world-model MPC planner is also evaluated); (2) a hybrid symbolic-neural architecture that solves K-map and truth-table problems algorithmically while specialized agents handle waveform timing and general RTL; (3) knowledge-augmented generation from a 321-pattern base plus 971 open-source reference implementations with focus-aware retrieval; and (4) hierarchical specification decomposition into dependency-ordered sub-modules with interface synchronization. On VerilogEval-Human, ChipCraftBrain achieves 97.2% mean pass@1 (range 96.15-98.72% across 7 runs, best 154/156), on par with ChipAgents (97.4%, self-reported) and ahead of MAGE (95.9%). On a 302-problem non-agentic subset of CVDP spanning five task categories, we reach 94.7% mean pass@1 (286/302, averaged over 3 runs), a 36-60 percentage-point lift per category over the published single-shot baseline; we additionally lead three of four categories shared with NVIDIA's ACE-RTL despite using roughly 30x fewer per-problem attempts. A RISC-V SoC case study demonstrates hierarchical decomposition generating 8/8 lint-passing modules (689 LOC) validated on FPGA, where monolithic generation fails entirely.

Reinforcement learning-based control policies have been frequently demonstrated to be more effective than analytical techniques for many manipulation tasks. Commonly, these methods learn neural control policies that predict end-effector pose changes directly from observed state information. For tasks like inserting delicate connectors which induce force constraints, pose-based policies have limited explicit control over force and rely on carefully tuned low-level controllers to avoid executing damaging actions. In this work, we present hybrid position-force control policies that learn to dynamically select when to use force or position control in each control dimension. To improve learning efficiency of these policies, we introduce Mode-Aware Training for Contact Handling (MATCH) which adjusts policy action probabilities to explicitly mirror the mode selection behavior in hybrid control. We validate MATCH's learned policy effectiveness using fragile peg-in-hole tasks under extreme localization uncertainty. We find MATCH substantially outperforms pose-control policies -- solving these tasks with up to 10% higher success rates and 5x fewer peg breaks than pose-only policies under common types of state estimation error. MATCH also demonstrates data efficiency equal to pose-control policies, despite learning in a larger and more complex action space. In over 1600 sim-to-real experiments, we find MATCH succeeds twice as often as pose policies in high noise settings (33% vs.~68%) and applies ~30% less force on average compared to variable impedance policies on a Franka FR3 in laboratory conditions.

Enforcing constraint satisfaction in neural network outputs is critical for safety, reliability, and physical fidelity in many control and decision-making applications. While soft-constrained methods penalize constraint violations during training, they do not guarantee constraint adherence during inference. Other approaches guarantee constraint satisfaction via a projection layer, but often rely on the existence of a tractable projection onto the feasible set, limiting their utility in more general problem settings. Many real-world problems of interest are nonlinear and lack the special structure admitting a tractable projection, motivating the development of methods that can enforce general nonlinear constraints. To this end, we introduce HardNet++, a constraint-satisfaction method that enforces linear and nonlinear equality and inequality constraints. Our approach iteratively adjusts the network output via damped local linearizations of the constraints. Each iteration is differentiable, admitting an end-to-end training framework, where the constraint satisfaction layer is active during training. We show that under certain regularity conditions, this procedure enforces nonlinear constraint satisfaction to arbitrary tolerance. Finally, we demonstrate tight constraint adherence without loss of optimality in a learning-for-optimization context, where we apply this method to a nonlinear model predictive control problem.

Modern world models are becoming too complex to admit explicit dynamical descriptions. We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator, conditioned on a context signal $ξ_t$. We develop a sample-based Penalized Predictive Control (PPC) framework grounded in online Riemannian optimization, in which the Simulator compresses the feasibility manifold into a score-based density $\hat{p}(u \mid ξ_t)$ that endows the action space with a Riemannian geometry guiding the Planner's gradient descent. The barrier curvature $κ(ξ_t)$, the minimum curvature of the conditional log-density $-\ln\hat{p}(\cdot\midξ_t)$, governs both convergence rate and safety margin, replacing the Lipschitz constant of the unknown dynamics. Our main result is a contextual safety bound showing that the distance from the true feasibility manifold is controlled by the score estimation error and a ratio that depends on $κ(ξ_t)$, both of which improve with richer context. Simulations on a dynamic navigation task confirm that contextual PPC substantially outperforms marginal and frozen density models, with the advantage growing after environment shifts.

Q-learning is a fundamental algorithmic primitive in reinforcement learning. This paper develops a new framework for analyzing Q-learning from a switching linear system (SLS) viewpoint. In particular, we derive a stochastic SLS representation of the Q-learning error, and a finite-time error analysis through the joint spectral radius (JSR) of the corresponding SLS model, where the JSR is the exact worst-case exponential rate of the associated SLS. To the best of our knowledge, this is the first convergence rate analysis of standard Q-learning whose leading exponential rate is expressed through the JSR. The resulting rate is tied to the intrinsic worst-case exponential rate of the direct SLS representation and can be sharper than row-sum upper bounds when those bounds are conservative.

We introduce the Cyber Defense Benchmark, a benchmark for measuring how well large language model (LLM) agents perform the core SOC analyst task of threat hunting: given a database of raw Windows event logs with no guided questions or hints, identify the exact timestamps of malicious events. The benchmark wraps 106 real attack procedures from the OTRF Security-Datasets corpus - spanning 86 MITRE ATT&CK sub-techniques across 12 tactics - into a Gymnasium reinforcement-learning environment. Each episode presents the agent with an in-memory SQLite database of 75,000-135,000 log records produced by a deterministic campaign simulator that time-shifts and entity-obfuscates the raw recordings. The agent must iteratively submit SQL queries to discover malicious event timestamps and explicitly flag them, scored CTF-style against Sigma-rule-derived ground truth. Evaluating five frontier models - Claude Opus 4.6, GPT-5, Gemini 3.1 Pro, Kimi K2.5, and Gemini 3 Flash - on 26 campaigns covering 105 of 106 procedures, we find that all models fail dramatically: the best model (Claude Opus 4.6) submits correct flags for only 3.8% of malicious events on average, and no run across any model ever finds all flags. We define a passing score as >= 50% recall on every ATT&CK tactic - the minimum bar for unsupervised SOC deployment. No model passes: the leader clears this bar on 5 of 13 tactics and the remaining four on zero. These results suggest that current LLMs are poorly suited for open-ended, evidence-driven threat hunting despite strong performance on curated Q&A security benchmarks.

Bimanual mobile manipulation requires a seamless integration between high-level semantic reasoning and safe, compliant physical interaction - a challenge that end-to-end models approach opaquely and classical controllers lack the context to address. This paper presents GenerativeMPC, a hierarchical cyber-physical framework that explicitly bridges semantic scene understanding with physical control parameters for bimanual mobile manipulators. The system utilizes a Vision-Language Model with Retrieval-Augmented Generation (VLM-RAG) to translate visual and linguistic context into grounded control constraints, specifically outputting dynamic velocity limits and safety margins for a Whole-Body Model Predictive Controller (MPC). Simultaneously, the VLM-RAG module modulates virtual stiffness and damping gains for a unified impedance-admittance controller, enabling context-aware compliance during human-robot interaction. Our framework leverages an experience-driven vector database to ensure consistent parameter grounding without retraining. Experimental results in MuJoCo, IsaacSim, and on a physical bimanual platform confirm a 60% speed reduction near humans and safe, socially-aware navigation and manipulation through semantic-to-physical parameter grounding. This work advances the field of human-centric cybernetics by grounding large-scale cognitive models into predictable, high-frequency physical control loops.

Extreme-edge scientific applications use machine learning models to analyze sensor data and make real-time decisions. Their stringent latency and throughput requirements demand small batch sizes and require that model weights remain fully on-chip. Spatial dataflow implementations are common for extreme-edge applications. Spatial dataflow works well for small networks, but it fails to scale to larger models due to inherent resource scaling limitations. AI Engines on modern FPGA SoCs offer a promising alternative with high compute density and additional on-chip memory. However, the architecture, programming model, and performance-scaling behavior of AI Engines differ fundamentally from those of the programmable logic, making direct comparison non-trivial and the benefits of using AI Engines unclear. This work addresses how and when extreme-edge scientific neural networks should be implemented on AI Engines versus programmable logic. We provide systematic architectural characterization and micro-benchmarking and introduce a latency-adjusted resource equivalence (LARE) metric that identifies when AI Engine implementations outperform programmable logic designs. We further propose spatial and API-level dataflow optimizations tailored to low-latency scientific inference. Finally, we demonstrate the successful deployment of end-to-end neural networks on AI Engines that cannot fit on programmable logic when using the hlsml toolchain.

Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering

We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear matrix-valued differential equation for each new system instance, we construct offline an approximation of the associated solution operator mapping time-dependent system parameters to the Riccati trajectory. The resulting model enables fast online evaluation of approximate optimal feedbacks across a wide class of systems, thereby shifting the computational burden from repeated numerical integration to a one-time learning stage. From a theoretical perspective, we establish control-theoretic guarantees for this operator-based approximation. In particular, we derive bounds quantifying how operator approximation errors propagate to feedback performance, trajectory accuracy, and cost suboptimality, and we prove that exponential stability of the closed-loop system is preserved under sufficiently accurate operator approximation. These results provide a framework to assess the reliability of data-driven approximations in optimal control. On the computational side, we design tailored DeepONet architectures for matrix-valued, time-dependent problems and introduce a progressive learning strategy to address scalability with respect to the system dimension. Numerical experiments on both time-invariant and time-varying LQR problems demonstrate that the proposed approach achieves high accuracy and strong generalization across a wide range of system configurations, while delivering substantial computational speedups compared to classical solvers. The method offers an effective and scalable alternative for parametric and real-time optimal control applications.

Safety filters have been shown to be effective tools to ensure the safety of control systems with unsafe nominal policies. To address scalability challenges in traditional synthesis methods, learning-based approaches have been proposed for designing safety filters for systems with high-dimensional state and control spaces. However, the inevitable errors in the decisions of these models raise concerns about their reliability and the safety guarantees they offer. This paper presents Adaptive Conformal Filtering (ACoFi), a method that combines learned Hamilton-Jacobi reachability-based safety filters with adaptive conformal inference. Under ACoFi, the filter dynamically adjusts its switching criteria based on the observed errors in its predictions of the safety of actions. The range of possible safety values of the nominal policy's output is used to quantify uncertainty in safety assessment. The filter switches from the nominal policy to the learned safe one when that range suggests it might be unsafe. We show that ACoFi guarantees that the rate of incorrectly quantifying uncertainty in the predicted safety of the nominal policy is asymptotically upper bounded by a user-defined parameter. This gives a soft safety guarantee rather than a hard safety guarantee. We evaluate ACoFi in a Dubins car simulation and a Safety Gymnasium environment, empirically demonstrating that it significantly outperforms the baseline method that uses a fixed switching threshold by achieving higher learned safety values and fewer safety violations, especially in out-of-distribution scenarios.

We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical patterns by timescale. By masking latents in the frequency domain during training, our method yields representations that can be manipulated coherently at inference. This allows us to generate musical variations and blends from reference examples while preserving characteristics at desired timescales, which are specified as frequencies in the latent space. LatentFT parallels the role of the equalizer in music production: while traditional equalizers operates on audible frequencies to shape timbre, LatentFT operates on latent-space frequencies to shape musical structure. Experiments and listening tests show that LatentFT improves condition adherence and quality compared to baselines. We also present a technique for hearing frequencies in the latent space in isolation, and show different musical attributes reside in different regions of the latent spectrum. Our results show how frequency-domain control in latent space provides an intuitive, continuous frequency axis for conditioning and blending, advancing us toward more interpretable and interactive generative music models.

What appears effortless to a human waiter remains a major challenge for robots. Manipulating objects nonprehensilely on a tray is inherently difficult, and the complexity is amplified in dual-arm settings. Such tasks are highly relevant to service robotics in domains such as hotels and hospitality, where robots must transport and reposition diverse objects with precision. We present DART, a novel dual-arm framework that integrates nonlinear Model Predictive Control (MPC) with an optimization-based impedance controller to achieve accurate object motion relative to a dynamically controlled tray. The framework systematically evaluates three complementary strategies for modeling tray-object dynamics as the state transition function within our MPC formulation: (i) a physics-based analytical model, (ii) an online regression based identification model that adapts in real-time, and (iii) a reinforcement learning-based dynamics model that generalizes across object properties. Our pipeline is validated in simulation with objects of varying mass, geometry, and friction coefficients. Extensive evaluations highlight the trade-offs among the three modeling strategies in terms of settling time, steady-state error, control effort, and generalization across objects. To the best of our knowledge, DART constitutes the first framework for non-prehensile dual-arm manipulation of objects on a tray. Project Link: https://dart-icra.github.io/dart/

A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some natural laws of motion,'' and can they be derived by an application of these laws? We explore this question by positing the theory that optimization algorithms may be considered as some manifestation of hidden algorithm primitives that obey certain universal non-Newtonian dynamics. This natural physics of optimization is developed by equating the terminal transversality conditions of an optimal control problem to the generalized Karush/John-Kuhn-Tucker conditions of an optimization problem. Through this equivalence formulation, the data functions of a given constrained optimization problem generate a natural vector field that permeates an entire hidden space with information on the optimality conditions. An action-at-a-distance'' operation via a Pontryagin-type minimum principle produces a local action to deliver a globalized result by way of a Hamilton-Jacobi inequality. An inverse-optimal algorithm is generated by performing control jumps that dissipate quantized ``energy'' defined by a search Lyapunov function. Illustrative applications of the proposed theory show that a large number of algorithms can be generated and explained in terms of the new mathematical physics of optimization.