Feedback Linearization

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.

Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In $320$ paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly $50\%$ to $6.2\%$, and reduces safety-violating runs from $118/160$ to $24/160$. In addition, across $52$ infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in $94\%$ of cases.

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

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

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

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

This paper studies incremental stability of holomorphic dynamical systems through the infinitesimal Kobayashi metric, an intrinsic pseudometric on complex manifolds invariant under holomorphic transformations and free of the coordinate dependence inherent in auxiliary Riemannian or Hermitian formulations. Contraction is formalized as an upper Dini-derivative inequality on the Kobayashi metric along trajectories; the passage from this differential condition to exponential distance contraction follows the classical Finsler-metric contraction mechanism of Forni and Sepulchre, instantiated here for the case in which the Finsler structure is the Kobayashi metric itself. Since the intrinsic condition is difficult to verify directly, a practical criterion is developed through a smooth Hermitian metric, the complex-Hermitian analogue of the classical real matrix contraction inequality: contraction with respect to such a metric implies intrinsic contraction on forward-invariant compact subsets, the two notions related through explicit local equivalence constants. Building on this, a Nagumo-type invariance result is established for Laplacian-coupled holomorphic networks, giving verifiable conditions for forward invariance in a class of systems not previously treated this way, and the framework extends to feedback-controlled holomorphic systems, with consequences for equilibria and periodic orbits following directly from intrinsic contraction. Numerical experiments on a network of coupled holomorphic oscillators verify the Hermitian condition analytically on a proven invariant set, and reveal that the observed synchronization rate substantially exceeds this guaranteed rate; the gap matches, to three decimal places, a closed-form combination of the node-wise rate and the network graph-Laplacian spectral gap, identified here as a target for a network-aware extension rather than resolved in full.

Adaptive rounding methods such as GPTQ, or equivalently Babai's nearest plane algorithm, round a real matrix to integers under a quadratic metric. They process the entries in a fixed order, one at a time, propagating each rounding error to the entries not yet processed through a triangular feedback matrix. We study the two-sided version of this task, in which fixed nonsingular basis matrices act on both the left and the right of the residual; the familiar one-sided case is the special case of an identity right basis. Vectorizing the matrix turns the two-sided objective into a quadratic metric whose Gram matrix is a Kronecker product, so the one-dimensional algorithm applies verbatim, but takes quartic time in the matrix dimension. We present GPTQ-2D, which produces the identical rounded matrix in cubic time. It rounds the entries anti-diagonal by anti-diagonal; entries on the same anti-diagonal are independent and are rounded in parallel.

At parking speeds, the kinematic bicycle is the prevailing model for car-like vehicles. Yet, despite its wide use, stabilizing feedback laws for this system are scarce in the literature, and existing designs often do not reproduce realistic parking maneuvers. This limitation is inherent to the Cartesian coordinates, where Brockett's condition rules out smooth static feedback stabilization. We bypass this obstruction by transforming the system into polar coordinates together with additional range-normalized coordinates that encode the geometry of human-like parking maneuvers. In the transformed coordinates, the dynamics take a strict-feedback form, enabling a nonconventional backstepping design. We exploit the particular structure to develop smooth feedback laws that achieve global exponential stabilization in the transformed coordinates which in turn generates parking trajectories resembling the one performed by human drivers through feedback alone.

Sonomyography (SMG) enables continuous device control via ultrasound-measured muscle deformation signals, but existing SMG interfaces generally require substantial user- and sensor-location-specific training data and provide only one proportional signal or task-specific classification. We present a real-time, sensor-placement-agnostic SMG control system based on sparse optical flow tracking that enables continuous 1-DOF control after minimal calibration (3 pose definitions). We also present a preliminary expansion of this method that augments this algorithm with a short computer-aided calibration to enable 2-DOF control. We evaluate both 1- and 2-DOF systems' performance for a preliminary cohort of 3 cervical spinal cord injury survivors and 6 uninjured individuals across 6 sensor placements spanning the arm, neck, and upper torso. As assessed by a cursor trajectory tracking task, all participants achieved continuous 1-DOF control at all tested sensor locations (even those that relied on passive tissue motions), with all participants achieving <5.5% tracking error using at least one placement (and many <4% across many). All participants were also able to modulate 2D cursor position via the 2-DOF system, with varying levels of control authority, and several were able to complete a 2D drawing task, constituting the first (to our knowledge) demonstration of location-agnostic multi-DOF continuous SMG-based control. These results highlight the promise of SMG to enable rapidly calibratable, high-dimensional, sensor-placement-agnostic device control by users with tetraplegia, and also illuminate key challenges in both signal processing and practical system deployment. To enable further development by scientific and user communities, developed algorithms have been open-sourced as part of the OpenMyoControl project on SimTK (simtk.org/projects/openmyocontrol).

A growing body of 2026 work applies control theory to LLM agents: Lyapunov-certified stability for tool-mediated controllers (Prinos et al., "Stable Agentic Control", 2026), sample-complexity bounds for sparse policies over massive discrete tool universes (Majumdar, "Sparse Agentic Control", 2026), and regulatory-control decompositions of multi-agent systems into auditable feedback loops (Nogueira and Skogestad, 2026). We do not claim to introduce control theory to LLM agents -- that ship has sailed. Our narrower claim is about what the controlled variable is. Prior work controls tool selection, inter-agent message routing, or the agent's raw action stream. We instead treat context assembly itself -- which prompt template, which few-shot demonstrations, how much retrieved context, how many planning/verification passes -- as the controlled variable, learned online by a contextual bandit or REINFORCE policy sitting outside a frozen model. This paper develops the formal decomposition (inner frozen policy $π_θ$, outer context policy $π_φ$), gives a stability argument for the online controller in the sense used by Zhang et al. (2026) (non-decreasing expected reward under bounded policy change), and reports an uncertainty-calibration analysis of the controller's own confidence against realized task outcomes. The applied counterpart to this paper instantiates the same controller across three domains and two model providers and releases the dataset, trajectory logs, and a deployment recipe; here we focus on the formal framing and the stability/uncertainty evidence a control-theoretic claim requires.

Bridging the sim-to-real gap is a central problem in robotics, and the prevailing approach is to build increasingly accurate simulators. Here, we propose another approach based on renormalization: using effective, resolution-dependent parameters to absorb details omitted by the simulator and reproduce real behavior. These parameters may differ from measured physical values because they compensate for what the simulator leaves out. We demonstrate this mechanism analytically for proportional--derivative (PD) control at finite simulation frequency, where proportional feedback changes the effective derivative gain and derivative feedback changes the effective inertia. We then interpret dynamic rope manipulation and underwater swimming through the same perspective. Finally, we present a practical procedure for choosing observables, identifying omitted physics, and determining effective parameters. Renormalization offers robotics a complementary path across the sim-to-real gap: effective parameters, real behavior.

We present a structured large-language-model-driven workflow for automated multi-variable control design from dynamic process models. The workflow decomposes the design task into constrained code-generation steps: plant-interface construction, normalization, manipulated-variable controlled-variable (MV-CV) pairing, controller specification, closed loop simulation, scenario generation, performance evaluation and Bayesian-optimization (BO) based tuning. Generated artifacts are executed and validated before downstream tasks proceed, and failed artifacts are repaired using validation feedback. The proposed approach is demonstrated on a nonlinear gas-preheater benchmark with coupled pressure and temperature dynamics. The generated workflow produces a physically consistent decentralized PI (proportional-integral) feedback-feedforward control structure and an executable tuning environment. Bayesian optimization reduces the closed loop performance objective, which aggregates set-point tracking and disturbance-rejection errors for the controlled variables, by approximately 26.5% relative to the initial controller generated by the workflow, mainly through improved pressure-loop transient performance. This figure quantifies the automated tuning stage rather than a comparison against a manually designed controller. The results demonstrate the feasibility of using structured large-language-model-based code generation to construct executable control-design workflows, while also highlighting the need for broader validation on larger plantwide-control benchmarks.

We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.

Fully actuated unmanned aerial vehicles (UAVs) are usually certified through rank conditions on a control-allocation matrix or through free-flight tracking performance. For aerial physical interaction, this certification may be incomplete. During sustained contact, part of the available wrench is consumed by the interaction task, and only the residual wrench remains available for stabilization, disturbance rejection, and maneuvering. This paper introduces a control-theoretic framework for \emph{contact-persistent full actuation}. A rigid-body model on $\R^{3}\times\SO\left(3\right)$ is combined with a morphology-dependent wrench map that captures fixed-tilt, variable-tilt, coaxial, and overactuated multirotor architectures. We define feasible wrench sets under actuator limits, residual wrench sets under task loading, and residual authority margins that strengthen the usual rank-based notion of full actuation. The main result shows that contact-persistent full actuation is equivalent to interiority of the task wrench in the constrained feasible wrench polytope, and that the residual authority radius is exactly the distance to the polytope boundary. We further introduce a signed residual-margin certificate for infeasible and boundary cases, a slack-maximizing allocation certificate, and a robust implementability condition that can be used as a margin-aware safety filter. Numerical evaluation on an abstract tilted hexarotor shows that full row rank alone does not imply feasible contact operation. Intermediate tilt angles preserve residual authority during pushing, whereas small or excessive tilts fail because of lateral-force deficiency or hover-margin loss.

Accurately steering a robot to a target configuration is fundamental in engineering, yet remains challenging for nonholonomic mobile robots. Vector fields (VFs) provide a natural framework by specifying desired motion directions throughout the workspace and enabling direct integration with feedback control. However, most existing VF-based methods cannot explicitly generate trajectories satisfying curvature constraints. Actuator limits are therefore often enforced by input saturation, which may invalidate stability guarantees and degrade closed-loop performance when not considered in controller design. In addition, these methods usually ensure only asymptotic convergence without an explicit settling-time bound. To address these issues, we propose a generalized motion planning and control framework consisting of a finite-time curvature-constrained vector field (FT-C2VF) and a saturation-free control law. Depending on the motion objective, the framework drives the robot to the target configuration in finite time or through it periodically. First, the FT-C2VF is constructed using complementary gains to achieve finite-time convergence while ensuring that the curvature of its integral curves is continuous, bounded, and monotonically decreasing with the radial ratio. Second, an almost globally C1-smooth, saturation-free controller is developed to track the FT-C2VF without Jacobian information, while keeping all control inputs within prescribed actuator limits. Third, dynamical-systems analysis establishes almost-global finite-time stability of the target equilibrium. Numerical simulations show improved performance over representative VF-based methods, and outdoor experiments on an Ackermann-steered vehicle confirm the effectiveness and robustness of the proposed approach.

This paper derives an analytical differential flatness transform for a tailsitter Unmanned Aerial Vehicle (UAV) under coordinated flight conditions using a simplified aerodynamic model. The proposed framework is formulated exclusively using rotation matrices, avoiding the ambiguities inherent to Euler angle representations. The method extends the applicability of an existing state-of-the-art differential flatness-based controller to flight regimes involving a significant vertical velocity component, where the previous approach becomes inapplicable. The proposed framework is validated experimentally with trajectories that highlight its advantages in these regimes.

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

Input--output feedback linearization fails at decoupling singularities, where the decoupling matrix loses rank, the relative degree is lost, and the linearizing control becomes unbounded. This paper develops a singularity-robust trajectory-tracking controller for square nonlinear control-affine systems that tracks through isolated decoupling singularities with bounded control. The method recasts tracking as real-time arc-length homotopy continuation, equivalently a continuous-time Newton/Davidenko flow, and replaces the inverse decoupling matrix by the least-norm Moore--Penrose solution of an augmented matrix $A=[Λ\mid b]$, where $b$ is the homotopy direction. A transversality condition $w^T b \ne 0$, with $w$ in the left null space of the decoupling matrix, keeps the augmented matrix full row rank through a generic rank-one loss. The resulting flow agrees with feedback linearization away from the singular set, tracks with $O(1/k)$ error, and re-locks after each crossing. The theory also characterizes the reflection-versus-branch-crossing dichotomy at Whitney folds and relates the reflection case to a Filippov sliding mode. Extensions cover dynamic relative-degree-one minimum-phase systems and arbitrary relative degree via filtered-error reduction. Simulations include a redundant 2-DOF manipulator, relative-degree-one and relative-degree-two plants, and a dual-active-bridge series-resonant DC/DC converter, where the method performs bounded inversion across buck/boost and resonance singularities while preserving zero-voltage soft switching.

Latent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single- or multi-step rollout loss on held-out data, as the training and model-selection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner's suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.

We study the optimal transport of optimally controlled agents from a compactly supported absolutely continuous source to a discrete target measure. The ground cost for the transport is induced by the optimal cost of the agents' motion. When this ground cost satisfies the twist condition, the optimal transport map is given almost everywhere in terms of a Laguerre tessellation of the state space. We refer to this control-theoretic generalization of Laguerre tessellation as Control Laguerre Tessellation (CLT), and illustrate it for two ground costs induced by linear controlled agents with minimum energy and minimum time objectives.

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.

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.

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.

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/

As robots move from controlled environments into real-world settings, it becomes increasingly crucial to ensure that they perform as expected. A key step toward that goal is a rigorous specification of the desired robot behavior, capturing intricate temporal, spatial, and logical requirements. Complementing this, plan and control synthesis methods are needed to fulfill these specifications with provable guarantees. This manuscript presents temporal logics - particularly linear and signal temporal logic - as expressive specification languages for robot behavior over time. We then discuss principles of formal synthesis, from discrete graph- and game-based approaches to sampling-based motion planning, trajectory optimization, and control-certificate-based synthesis. Finally, we outline challenges in deploying formal synthesis in real-world robotics, emphasizing the interplay between modeling fidelity, computational tractability, and the types of rigorous guarantees that can be achieved.

A control framework is proposed for safe local navigation of mobile robots equipped with Ackermann steering in unmapped environments where a global goal is absent. Based on local obstacle detections, the safest heading angle is determined along the direction of the largest open space ahead of the vehicle. Guided by this direction, bounding lines are constructed on the left and right sides of the vehicle to achieve obstacle separation. These bounding lines are obtained by solving a convex quadratic optimization that maximizes vehicle-to-obstacle clearance. Optionally, conditions are imposed on the bounding lines to preserve parallelism and smooth abrupt changes from prior control steps. A feedback-linearizing controller is then used to regulate the vehicle's distance from one or both bounding lines, effectively enabling tracking of a local reference path that preserves safety through obstacle clearance maximization. Open-source code is included for the application of this control scheme. Experimental results demonstrate that the proposed method produces safer navigation paths with significantly shorter computation times, compared to some existing exploration-based planners.

Transformer-based architectures have significantly advanced the generation of complex symbolic sequences, yet a significant gap remains in achieving fine-grained, interpretable control over discrete signal attributes. This paper investigates the mechanistic interpretability of the Multitrack Music Transformer (MMT) and proposes a framework for deterministic attribute modulation without retraining to bridge this gap via inference-time activation steering. Utilizing the Difference-in-Means (DiffMean) methodology, we isolate latent directions for signal attributes, specifically Pitch and Duration, within the residual stream. We validate the Linear Representation Hypothesis in this domain, achieving high correlation between steering magnitude and attribute shift. To address the inherent feature entanglement in multi-attribute steering, we introduce a Dual Steering framework utilizing Gram-Schmidt Orthogonalization. Experimental results demonstrate that this geometric decoupling reduces conceptual interference and signal degradation compared to naive vector addition, enabling independent deterministic control even against strong autoregressive conditioning.

Reusing a held-out benchmark adaptively should, in principle, invite overfitting. Yet benchmark-driven machine learning (ML) has produced surprisingly little overfitting in practice. An attractive hypothesis is that successful ML strategies are highly compressible. We study this in the setting of LLM-driven research agents, where the hypothesis becomes directly testable via two complementary information bottlenecks. In \emph{output compression}, an exploration agent adaptively searches for high-performance models using a validation set, and we test whether a fresh ``reproducer agent'' can reproduce its performance given only an extremely short prompt and the training data. In \emph{input compression}, the explorer receives only one-bit feedback indicating whether each submitted model improves on the running best. Across 8 datasets spanning tabular classification, vision, language modeling, diffusion modeling, and reward modeling, we find that these bottlenecks have little effect on performance: short prompts and compressible feedback are sufficient to reproduce and find high-performance models. The hypothesis is falsifiable: when we deliberately induce validation-set overfitting, the results fail to reproduce with short prompts. Taken together, our results support a description-length explanation for the lack of overfitting in benchmark-driven ML: successful strategies occupy a low-complexity region of strategy space.

Tuning controllers for strongly coupled multi-input multi-output (MIMO) industrial processes is hard: decentralized classical auto-tuning ignores loop interaction, and local numerical optimization from natural initializations stalls in the resulting non-convex cost landscape. We ask whether on-premise open-source large language models (LLMs), which keep data on-site and need no plant model, can help. On a single-loop CSTR, classical relay-feedback tuning (IAE 0.106, near the 0.102 optimum) beats an LLM tuner (0.162): for simple loops the LLM adds nothing. The picture inverts on a strongly coupled quadruple-tank with conflicting set-points, scored by a penalized cost J = IAE + lambda*TV(u) that rewards tracking without chattering actuators. There, naive relay tuning (J ~ 28.6) and naive LLM tuning (29.7) are no better than open loop (22.7), and a local optimizer from balanced starts fails in 10/10 runs. A scaffolded open LLM instead reasons about the coupling, proposes the counter-intuitive asymmetric structure, and reaches J ~ 16.9 +/- 0.2 from any start; refining it with a classical optimizer attains the smooth global optimum (J ~ 12.0, 10/10 vs. 0/10), which even applies a non-obvious negative integral correction decentralized tuning cannot. A global optimizer (differential evolution) also reaches this optimum, so the LLM is not the only route; its advantage is sample efficiency and interpretability: a usable controller in 18 evaluations (where the global optimizer is worse than open loop) plus a stated rationale. This edge grows with dimension, reaching ~6x fewer evaluations on a 3x3 plant. The behaviour generalizes across four open models, and on a benign plant the LLM offers no advantage, sharpening the boundary. We contribute a reproducible benchmark delimiting when open LLMs help in control tuning: not as optimizers, but as a sample-efficient, interpretable structural prior.

Time-of-flight cameras are popular in robotics because they provide direct depth information and are compact, inexpensive, and less dependent on ambient visible light. However, their low spatial resolution and depth noise raise questions about their suitability for stabilizing fast, unstable dynamics. In this paper, we show that an inexpensive, low-resolution time-of-flight camera can provide angle feedback for reliable and precise balancing of an inverted pendulum on a cart, a canonical control benchmark. These results open the door to using compact, inexpensive, low-resolution time-of-flight cameras for precise feedback control of fast, unstable systems.

This paper addresses orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model within a transverse-linearization framework. We show that the corresponding transverse linearization is unstable and not stabilizable by linear state feedback. Therefore, the standard linearization-based approach to orbital stabilization cannot be applied directly. The main contribution is a set of explicit and verifiable conditions that characterize when a controller design based on transverse linearization remains applicable. These conditions rely on the specific structure of the dynamics in a neighborhood of the motion and on the use of non-standard transverse coordinates for controller design and analysis. Numerical simulations illustrate the proposed design procedure.

Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness. However, standard primal--dual methods struggle to update multipliers robustly under stochastic mini-batch feedback, as the noise of mini-batch gradients and constraint estimates can be directly accumulated into the multiplier memory. To address this issue, we propose Residual-Controlled Multiplier Learning (RCML), which reformulates multiplier updating as projected-pressure feedback. The central idea is to decompose the projected multiplier into an effective pressure signal for primal descent and a pressure-memory residual for finite-gain multiplier tracking. To handle heterogeneous and noisy observations, we further augment this residual-integral backbone with modular stochastic stabilization components. For the convex-affine backbone, we establish finite-gain convergence, derive a stochastic residual bound under mini-batch feedback, and show that the residual feedback law admits a local KKT-residual interpretation near regular KKT points of nonconvex problems. Experiments across optimization, allocation, and fair-ranking tasks show that RCML improves feasibility control and multiplier stability while maintaining competitive objective performance. Code is released at https://anonymous.4open.science/r/RCML-3114/.

We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.

Signal Temporal Logic (STL), has recently seen extensive development, owing to its rich expressivenes for autonomous planning and control. Nevertheless, existing verification and control synthesis methods are limited with respect to the complexity and degree of nesting of the formulae. In this work, we propose a novel approach to STL based on an operator acting on reachability value functions. This constitutes a new theoretical framework for handling complex multi-nested formulae while at the same time providing tools for on-line control synthesis. In contrast to focusing on the design of STL-based reachability (or control barrier) functions, we develop operator-based nesting rules directly. Our method's expressiveness is demonstrated both theoretically, where necessary and sufficient conditions for STL formula satisfaction are extracted, as well as in simulations with complex fragments.

Optimizing HVAC (Heating, Ventilation and Air Conditioning) can enhance a building's energy efficiency while providing comfort levels for its occupants. Using conventional control systems to maintain HVAC functions is often difficult because of the nonlinear characteristics of a building envelope as it experiences stochastic load variations over time. This paper presents a new approach to optimizing HVAC systems through the use of Deep Reinforcement Learning (DRL) algorithms and the Proximal Policy Optimization (PPO) algorithm implemented in a custom Python performance environment. The DRL system uses a second order resistor-capacitor thermal model and an integrated dynamic mass balance of CO2 to replicate the complex physics associated with buildings. One major innovation of this study is a "Hierarchical Flow Logic," which provides the means to ensure that indoor air quality (IAQ) is maintained by overriding the accepted actions of the agent that cause CO2 to exceed 1000 ppm. In addition, an enthalpy-based economiser is used to create free cooling from the outdoor environment. The experimental data shows that compared to PID controllers tuned by GA or traditional On-Off controls, a PPO agent has better temperature stability and energy efficiency overall. An end-to-end pipeline provides an avenue for robust and generalized solutions to help implement smart building energy management within the context of real hardware implementation.

Controlling physics-based humanoids from natural-language instructions is a critical step toward general-purpose embodied agents. However, existing methods remain constrained by a tension between semantic expressiveness and physical feasibility, often failing to jointly achieve faithful instruction following, high-quality motion, and stable long-horizon control. We propose SCRIPT, a scalable diffusion policy with a multi-stage training framework for language-driven physics-based humanoid control. The core of SCRIPT is a Joint Action-State-Text Diffusion Transformer (JAST-DiT), which represents actions, physical states, and text as dedicated token streams and couples them through joint attention, enabling direct interaction between language semantics and control dynamics. To stabilize autoregressive control, we introduce a nonlinear history conditioning mechanism, which preserves the dense recent context and samples increasingly sparse cues from long-term history. Beyond supervised imitation pre-training, we propose a post-training stage, further improving the performance using Reinforcement Learning with Hybrid Rewards (RLHR). By injecting learnable noise into the flow-sampling process, RLHR effectively improves motion quality and instruction following within closed-loop simulations using hybrid physical feedback and text rewards. Quantitative evaluations demonstrate that SCRIPT outperforms prior state-of-the-art methods, with gains across text alignment, motion quality, and physical realism metrics. Furthermore, scaling studies on the 1200-hour MotionMillion dataset demonstrate consistent performance gains with model scaling, highlighting SCRIPT's robust scalability for large-scale pre-training. Our code will be publicly available for future research.

This paper presents a low-complexity, model-free, output-feedback controller for a class of unknown time-varying nonlinear systems with unknown input constraints. The controller achieves the preset control accuracy when the actuator is not saturated and maintains flexible control accuracy after actuator saturation. This result extends existing constraint control methods for linear manifolds to a more general form, including the construction of nonlinear manifolds and various types of constraints, thereby achieving preset control accuracy within finite or fixed time. Additionally, flexible control under unknown saturation is achieved through the construction of an error-driven flexible constraint. Finally, second-order and higher-order control examples and simulations are provided.

LLM discovery and optimization systems are increasingly applied across domains, implementing a common propose-evaluate-revise loop. Such optimization or discovery progresses via context conditioning on received feedback from an environment. However, as modern LLM agents are increasingly complex in their structure, it is difficult to evaluate which components contribute the most, and when and how this exploration may fail. We answer these questions through three controlled experiments. Our findings: (1) In pure black-box optimization, LLMs act as greedy optimizers. (2) In zero-shot kernel generation, providing explicit input-size information has no measurable effect, models converge to the same kernel parameters regardless of size or temperature, as though the size instruction were invisible. Moreover, when tasked to perform kernel optimization for uncommon kernel sizes, performance sharply degrades regardless of the language used. (3) In feedback-loop kernel optimization, CUDA improves monotonically under iterative feedback, while TVM IR actively degrades, which demonstrates that kernel optimization degrades when models operate with low-density language. Our results conclude that LLMs in code optimization tasks highly depend on pretrained priors rather than provided feedback or agentic structure.

Reinforcement learning often produces high-frequency oscillatory control signals that undermine the safety and stability required for physical deployment. Explicit action chunking addresses this by predicting fixed-horizon trajectories but scales the policy output dimension proportionally with the horizon length, leading to optimization difficulties and incompatibility with standard step-wise interaction. To overcome these challenges, this paper proposes Dual-Window Smoothing (DWS), an implicit action chunking framework for smooth continuous control. Unlike explicit methods, DWS enforces temporal coherence without expanding the action space. It uses a dual-window design: an execution window that ensures physical smoothness through deterministic modulation, and a value window that aligns temporal-difference targets over the horizon to correct critic bias caused by open-loop execution. DWS also includes a lightweight actor-side temporal regularizer based on first-order action differences to promote global continuity. This design effectively bridges the gap between temporal abstraction and reactive step-wise control. Experiments on benchmarks including the DeepMind Control Suite and industrial energy management tasks show that DWS outperforms state-of-the-art (SOTA) baselines. In complex vision-based autonomous driving tasks, DWS achieves smoother control, safer behavior with reduced jitter, and attains a 100% success rate.

Safe exploration remains a fundamental challenge in reinforcement learning (RL), limiting the deployment of RL agents in the real world. We propose Sampling-Based Safe Reinforcement Learning (SBSRL), a model-based RL algorithm that maintains safety throughout the learning process by enforcing constraints jointly across a finite set of dynamics samples. This formulation approximates an intractable worst-case optimization over uncertain dynamics and enables practical safety guarantees in continuous domains. We further introduce an exploration strategy based on constraining epistemic uncertainty, eliminating the need for explicit exploration bonuses. Under regularity conditions, we derive high-probability guarantees of safety throughout learning and a finite-time sample complexity bound for recovering a near-optimal policy. Empirically, SBSRL achieves safe and efficient exploration both in simulation and in real robotic hardware, and readily extends to practical deep-ensemble implementations that scale to high-dimensional continuous control problems.

Robotic systems are vulnerable to False Data Injection Attacks (FDIAs), where adversaries corrupt sensor signals to gain malicious control. Feedback linearization exposes robotic systems to integrator vulnerability, making them susceptible to stealthy attacks that can cause significant deviations in end-effector behavior without raising alarms. This paper addresses the resilience of manipulators against finite-horizon FDIAs by formalizing two defense methods, namely anomaly-aware virtual damping and manipulability reduction, with probabilistic guarantees on nominal task execution. Simulations on a 7-DOF redundant manipulator show that the proposed defenses substantially reduce the impact of FDIA compared to using solely a threshold-based ADS like the Chi-squared, while preserving nominal task performance in the absence of attack.

Flexible robotic manipulators (FRMs) offer advantages in lightweight design and large workspace, but their structural flexibility induces vibrations, accelerates fatigue, degrades tracking performance, and limits operational speed. These challenges are further amplified in multi-link serial manipulators, where increased overall length leads to greater structural flexibility. This article presents a backstepping output-feedback framework for fast vibration suppression and tip tracking of an n-degree-of-freedom serial flexible manipulator robot (nDSFMR), with a DeepONet-based approximation for practical deployment. Each link-joint is modeled as a Timoshenko beam coupled with an ODE and transformed into a canonical hyperbolic PDE with boundary dynamics. A backstepping-based boundary controller at the joint is developed to equivalently inject distributed damping along the beam, enabling rapid vibration suppression and trajectory tracking, only using available boundary measurements. To enable real-time implementation and scalability, a DeepONet neural operator is introduced to approximate the backstepping kernels, significantly reducing computational cost and facilitating fast controller updates under varying operating conditions. Experiments on a two-link flexible manipulator demonstrate faster vibration suppression and convergence of the end-effector to the desired trajectory, compared with a linear quadratic regulator (LQR) with feedforward control.

Decentralized federated learning (FL) is a promising approach for training machine learning models on sensor networks, Internet of Things (IoT) devices, and other edge systems where no central server exists. While federated learning offers advantages such as preserving data privacy, it often suffers from non-independent and identically distributed (IID) data distributions across devices, which cause significant performance degradation. This issue is particularly severe when directly optimizing model parameters, because neural network training is inherently non-convex and standard convergence guarantees for convex optimization do not apply. Unlike existing decentralized FL methods that primarily operate in parameter space, we propose federated function-space alternating direction method of multipliers (FedF-ADMM). FedF-ADMM exploits the convexity of loss functionals within function space to derive alternating direction method of multipliers (ADMM)-based update directions, which are subsequently projected onto the parameter space via knowledge distillation. We further introduce a stabilization coefficient to enhance robustness under severe non-IID settings and analyze its behavior from a control-theoretic perspective by interpreting it as a proportional-integral (PI) term. Experiments under challenging non-IID scenarios, including settings where each device has data from only a single label, demonstrate that FedF-ADMM achieves faster and more stable convergence than existing decentralized FL methods, while attaining higher accuracy and better consensus among devices.

Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs), but standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights. This often leads to ill-conditioning, sensitivity to loss weights, and poor constraint satisfaction. In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP). The key idea is to view the constraint residuals as the output of a controlled dynamical system and to compute the Lagrange multiplier as a feedback input that locally drives these residuals toward stable linear contraction dynamics. AdamFLIP then applies Adam-style first- and second-moment adaptation to the resulting feedback-linearized Lagrangian gradient, combining principled constraint handling with the scalability and robustness of adaptive neural-network optimization. We test AdamFLIP on a range of benchmark forward and inverse PDE problem, and it consistently outperforms both the standard soft-constrained PINN and state-of-the-art constrained optimizers. Specifically, on the Navier--Stokes equations benchmark, AdamFLIP \textbf{reduces relative $L_2$ error by more than two thirds} for the predicted solution compared to the next best method. Our AdamFLIP framework provides an effective and computationally scalable hard constraint optimization method for PINN training.

Tokamaks remain leading candidates for achieving practical fusion energy, yet many important control problems inside these devices are still difficult or unsolved. One such challenge is controlling the plasma rotation profile, which strongly influences stability, confinement, and transport. While the average rotation can be controlled, controlling the full profile is challenging due to high dimensionality, response to multiple actuators and dependence on plasma condition. Learning-based control methods, such as reinforcement learning (RL), provide a potential solution to this challenging problem with ability to model complex interactions leading to effective multi-input multi-output control. However, learning such policies is challenging due to the lack of accurate simulators that can model the rotation profile dynamics. In this work, we investigate the use of offline RL and offline model-based RL algorithms for rotation profile control, training them solely on historical data from the DIII-D tokamak. Our final method uses probabilistic models of plasma dynamics to generate rollouts for RL training. We deploy this policy on the DIII-D Tokamak and observe promising real-world results. We conclude by highlighting key challenges and insights from training and deploying an RL policy on a complex physical device while using only limited past data.

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.

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.

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.

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.

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.

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.

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.

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.

This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50% lower angular control effort compared to the baseline.

Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strength of both paradigms by estimating the coefficients of a low-dimensional Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector directly amenable to model-based control, while retaining the modularity, probabilistic treatment and computational efficiency of factor graph inference. The proposed method is evaluated in simulation on a 0.4 m long tendon-driven continuum robot under three measurement configurations, achieving mean position errors below 2 mm for all three scenarios and demonstrating a sixfold reduction in orientation error compared to a Gaussian process regression baseline when only position measurements are available.

Fundamental limits on the performance of feedback controllers are essential for benchmarking algorithms, guiding sensor selection, and certifying task feasibility -- yet few general-purpose tools exist for computing them. Existing information-theoretic approaches overestimate the information a sensor must provide by evaluating it against the uncontrolled system, producing bounds that degrade precisely when feedback is most valuable. We derive a lower bound on the minimum expected cost of any causal feedback controller under partial observations by applying the Gibbs variational principle to the joint path measure over states and observations. The bound applies to nonlinear, nonholonomic, and hybrid dynamics with unbounded costs and admits a self-consistent refinement: any good controller concentrates the state, which limits the information the sensor can extract, which tightens the bound. The resulting fixed-point equation has a unique solution computable by bisection, and we provide conditions under which the free energy minimization is provably convex, yielding a certifiably correct numerical bound. On a scalar LQG problem the self-consistent bound captures over 80% of the known optimal cost at moderate sensor noise, and on a nonlinear Dubins car tracking problem it remains informative across all noise levels where a bound using the uncontrolled state distribution is vacuous.

This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental equivalences between different model representations, we are able to close the gap of control system operator learning and infinite-dimensional regression, enabling various empirical estimators and the connection to the well-understood learning theory in RKHSs under one unified framework. Consequently, our proposed framework allows for arbitrarily accurate finite-rank approximations in infinite-dimensional spaces and leads to finite-dimensional predictors without a priori restrictions to a finite span of functions or inputs. To enable applications to high-dimensional control systems, we improve the scalability of our proposed control Koopman operator estimates by utilizing sketching techniques. Numerical experiments demonstrate superior prediction accuracy compared to bilinear EDMD, especially in high dimensions. Finally, we show that our learned models are readily interfaced with linear-parameter-varying techniques for model predictive control.