Data-Driven Control

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.

Adaptive Cruise Control (ACC) systems are typically calibrated for an average driver, often resulting in a mismatch between vehicle behavior and individual expectations during time-critical maneuvers such as highway overtaking. When the ACC is perceived as too conservative and inconsistent, drivers intervene through throttle overrides, providing implicit feedback on the system's behavior. This paper reframes these override actions as human-in-theloop supervisory signals and proposes a data-driven framework for personalized vehicle adaptation, termed Context-driven Personalized ACC (CoP-ACC). Rather than relying solely on end-to-end regression, which tends to over-smooth dynamic responses, we introduce a hybrid pipeline combining: (i) unsupervised hierarchical clustering to extract representative acceleration profiles from override events; (ii) a context classifier that maps pre-maneuver driving conditions to the appropriate profile; and (iii) a residual regressor that refines the selected profile into a smooth, personalized acceleration profile tailored to the immediate context. Evaluated on real-world public-road data against a withheld forced-ACC baseline, the approach demonstrates high reconstruction fidelity and generates acceleration profiles that tend toward the driver's expected behavior in potential override contexts. The results highlight the potential of learning from shared-control overrides to enable anticipatory, personalized ACC behavior, reducing manual interventions and improving ride comfort.

Data-driven model predictive control (MPC) combines learned world models with online trajectory optimization, achieving strong performance in continuous control. However, the per-step cost of sampling and evaluating hundreds of candidate trajectories restricts deployment to control frequencies well below what real-time robotics demands. Motivated by the dual-process theory of human cognition, which distinguishes between fast, intuitive processing (System 1) and slower, deliberative reasoning (System 2), we ask whether every decision requires the same degree of computational deliberation. We propose Fast-TD-MPC, a lightweight framework that adaptively routes between fast policy execution and test-time planning, reserving costly deliberation for states where it is most needed. Fast-TD-MPC delivers competitive task performance across 103 continuous control tasks while achieving up to ~4x faster inference. Under external disturbances, Fast-TD-MPC selectively falls back to planning, maintaining robustness comparable to the original planner.

The repeated forward-reverse maneuvers performed by wheel loaders during earthmoving operations make them well suited for automation. However, the nonlinear dynamics of articulated vehicles and complex vehicle-terrain interactions limit the effectiveness of conventional model-based approaches. This paper presents a hierarchical framework that combines long-horizon geometric planning with data-driven predictive control for autonomous wheel-loader operation. A reduced-order articulated kinematic model is used to generate the maneuver geometry, where the forward and reverse trajectories are jointly optimized through a shared intermediate state. To capture the vehicle dynamics, two data-driven deep bilinear Koopman models are learned for the forward and reverse motions using data generated from high-fidelity simulations in Algoryx Dynamics. The learned Koopman representations are subsequently incorporated into a computationally efficient model predictive control (MPC) formulation for trajectory tracking. The resulting controller operates in real time within a 50-ms execution loop. High-fidelity simulation results demonstrate that the proposed end-to-end framework enables accurate and computationally efficient execution of wheel-loader V-cycle maneuvers, providing a promising approach toward autonomous operation of articulated heavy-duty machinery.

The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.

Ground-truth human joint torque estimation relies on motion capture systems, which suffer from limited outdoor usability and significant deployment expenses. Furthermore, direct scaling of ground-truth joint torques to obtain motor torque commands is not necessarily the optimal strategy. To address the aforementioned limitations, inspired by the human motion generation process, this paper proposes a novel assistance torque estimation method based on the dynamic model. From an optimization perspective, the proposed method directly generates motor-assist torque and lowers the cost of data acquisition. Then, a data-driven assistance torque prediction network is trained to enable accurate real-time prediction under complex outdoor environments. Experimental results demonstrate that optimized (estimated) assistance torque exhibits better phase consistency with gait trajectories and better alignment with task characteristics. Relative to the Zero torque condition, the predicted torque can decrease metabolic rate by 11.8%-17.7%, heart rate by 8.9%-14.3%, and peak muscle activation levels by 28.2%-54.0%, respectively. This provides a new perspective for low-cost adaptive exoskeleton assistance.

Agent-based model predictive control (AMPC) has recently been proposed for vehicle systems with various controllers, such as differential braking and torque vectoring, where controllers are regarded as distributed agents contributing to the same objective. However, this scheme is challenging in handling multiple conflicting objectives with coupled agents. A common approach for such tasks is the integrated MPC, where all objectives and agents are stacked together in one optimization. Nevertheless, as more agents and objectives are involved, the integrated MPC will face challenges like computational burdens and maintenance difficulties in practice. To this end, this paper proposes a learning multi-objective AMPC that can improve design flexibility and computing efficiency. First, under the assumption of information exchange, a multi-objective AMPC tailored from the alternating direction method of multipliers (ADMM) is proposed to decouple the system and achieve the same performance as the integrated scheme iteratively. Second, a learning-based method for initializing iterations is proposed to accelerate convergence. In addition, a data management method is proposed for real-time efficiency, and an authentication module is designed for learning reliability. We compare the proposed scheme against the integrated scheme via a combined path-tracking simulation for autonomous vehicles with various controllers. The proposed scheme achieves the same control performance as the integrated one while reducing the computational time by 43.5%. Furthermore, the learning-based method saves 88.6% more computational time than without learning, making it suitable for real-time implementation.

A finite-difference bowed-string model with implicitly resolved Stribeck friction is presented, with a regime diagnostic. Without implicit resolution no stick phase forms at any bow force. With friction, impedance and quality factor from published measurement rather than fitted, all four strings return a stick fraction of 89.1% against an ideal 90%. Schelleng's maximum bow force is recovered on every string. His minimum, $F_{\min} \propto Z^2 v_b β^{-2}$, is replaced by a law, $F_{\min} = C Z v_b / β$ with a dimensionless $C = 1.112 \pm 0.017$ that reproduces on sixty-four held-out operating points. Six controllers at matched capacity, on four strings at twenty seeds, place a gated recurrent network ahead of a feedforward one, its margin over the mean of the other five largest when the commanded bow speed is overridden at mid-stroke. The feedforward network completes more strokes, mostly from a cold start no player would use. A minimal gated variant fails because gates computed from the input alone cannot clear a latched state. Training loss selects neither the capacity nor the context length. No learned controller improves on the lookup rule that generated its labels where that rule is correct. Of the rule's 1089 cells, 57 are playable on a properly settled plant and unplayable by its labels, and the controller commands them where the lookup will not. The controller's score regresses on the rule's with a slope of 0.32, more than ten standard errors below unity, so it overtakes the rule where the rule fails and is bounded by it where it holds. Under a rigid finger stop the plant is provably invariant, so transfer loss between pitches is the controller's alone, traced to one feature. A regime classifier without a stick test mistakes small-amplitude periodic slipping for Helmholtz motion, and a harmonicity measure rates a string the bow never grips above it.

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

Reinforcement learning and control theory are two adjacent scientific fields that focus on optimizing the controller of unknown dynamical systems using feedback. While both fields have common roots in dynamic programming, they have evolved with distinct methodologies, goals, and cultures. Despite decades of mutual influence, a significant gap persists between the two communities. This tutorial introduces adaptive control, actor-critic reinforcement algorithms, and a new way to combine these two paradigms for data-driven decision making on a classical locomotion control problem. Our aim is to provide a foundation for understanding the core differences between the two approaches and insights to help experts in each field better understand and engage with the tools and approaches of the other.

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

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

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

Contact-rich manipulation requires force sensitivity, but many robot arms lack dedicated force sensors due to their high cost. We present Neural External Torque Estimation (NEXT), a data-driven method that estimates external joint torques without needing any dedicated force sensors. NEXT trains in 1 minute from only 10 minutes of free-motion data, yet achieves estimates comparable to dedicated joint-torque sensors. NEXT enables force-feedback teleoperation on low-cost arms and improves policy learning through Force-Informed Re-Sampling Training (FIRST), which up-samples pre-contact and contact segments during behavior cloning. Across five long-horizon tasks, FIRST outperforms prior force-aware policies by over 17% in task progress. Together, NEXT and FIRST bring force-aware teleoperation and policy learning to off-the-shelf robots without additional sensing hardware. Video results and code are available at https://jasonjzliu.com/factr2

In this paper, we consider a class of networked systems comprising an interconnected set of linear subsystems, disturbance inputs, and performance outputs. Using dissipativity theory, we first propose a model-based hierarchical control design strategy to ensure the closed-loop networked system is dissipative from its disturbance inputs to performance outputs. This involves designing local controllers for each subsystem to enforce local dissipativity guarantees, which are then exploited to co-design distributed global controllers and the interconnection topology to enforce global dissipativity guarantees while optimizing interconnection topology costs. The overall design process requires only solving a sequence of linear matrix inequality (LMI) problems, thereby retaining compositionality and decentralizability while avoiding non-convex, iterative design processes that are inefficient and centralized. This model-based hierarchical control design strategy assumes the knowledge of the subsystem dynamics, which may not hold in many real-world networked systems. Motivated by this, we also propose a data-driven hierarchical control design strategy that assumes only the availability of rich input-state-output trajectory data from the subsystems. The proposed data-driven design process assumes that the unknown disturbances affecting the subsystem dynamics are bounded by a quadratic matrix inequality (relaxing conventional bounds) and accounts for this by using the matrix S-lemma. Finally, the effectiveness of the proposed model-based and data-driven hierarchical control designs is illustrated for a networked system representing a DC microgrid, with the aim of enforcing robust (dissipative) voltage regulation and current sharing.

This paper presents the real-time retargeting guidance policy developed for the Chandrayaan-3 lunar landing mission. The baseline guidance generates approximate fuel-optimal descent trajectories, while a high-level policy enables safe retargeting to alternate sites when the nominal site becomes infeasible. The retargeting strategy leverages a convex representation of the controllability boundary, allowing rapid feasibility checks and real-time target updates. To the best of the authors knowledge, this represents the first application of a data-driven retargeting framework in an operational lunar landing mission. Pre-flight simulations and Chandrayaan-3 flight results validate the effectiveness of the proposed approach.

This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.

With the growth of the construction industry and the global shortage of skilled labor, the automation of crane control has become increasingly important for safe and efficient operations. A central challenge in automatic crane control is the reduction of load oscillations during motion, which is primarily addressed through appropriate slewing trajectories. In this context, classical model-based control methods rely on accurate dynamical models and expert tuning, and often struggle to meet safety and precision requirements, while many learning-based approaches require large data sets and significant computational resources. This paper proposes a behavioral data-driven framework for generating open-loop slewing trajectories for rotary cranes that suppress load sway while reducing operation time and energy consumption. The approach builds on Willems' fundamental lemma and its generalizations, to bypass explicit system modeling and operate directly on measured input-output data. A practical workflow is presented in this paper to reduce the need for expert knowledge. Despite the underactuated nature of the crane dynamics, the method identifies a nonparametric representation of the system behavior and generates smooth, optimal trajectories using limited data and convex optimization. The proposed trajectory generation method is validated on a laboratory crane setup and compared against an established model-based approach, achieving up to 35% reduction in load sway, 43% reduction in tracking error, and 50% reduction in travel time.

We study inventory control with decision-dependent censoring, focusing on the censored or repeated newsvendor (R-NV), where each order quantity determines whether demand is fully observed or censored by sales. Existing approaches based on parametric Thompson sampling (TS) can be brittle under prior mismatch, while offline imputation methods need not transfer to online learning. Motivated by the predictive view of decision making, we combine these ideas by taking oracle actions on learned completions of latent demand. We propose in-context generative posterior sampling (ICGPS), which uses modern generative models that are meta-trained offline and deployed online by in-context autoregressive generation. Theoretically, we show that the Bayesian regret of ICGPS with a learned completion kernel is bounded by the Bayesian regret of a TS benchmark with the ideal completion kernel plus a deployment penalty scaling as $\sqrt{T}$ times the square root of the completion mismatch. This yields a plug-in template for operational problems with known TS regret bounds. For R-NV, we derive sublinear Bayesian regret by reducing censored feedback to bandit convex optimization feedback. We also show that, under reasonable coverage and stability assumptions, the online completion mismatch is controlled by the offline censored predictive mismatch, so offline predictive quality transfers to online performance. Practically, we instantiate ICGPS with ChronosFlow, which combines a frozen time-series transformer backbone with a trainable conditional normalizing-flow head for fast censoring-consistent sampling. In benchmark experiments, ChronosFlow-ICGPS matches correctly specified TS, outperforms myopic and UCB-style baselines, and is robust to prior mismatch and distribution shift. ChronosFlow-ICGPS also performs well for the real-world SuperStore dataset, especially under heavy censoring.

We present a flow-matching planner for autonomous driving that directly outputs actionable control trajectories defined by acceleration and curvature profiles. The model is conditioned on a bird's-eye-view (BEV) raster of the surrounding scene and generates control sequences in a small number of Ordinary Differential Equations (ODE) integration steps, enabling low-latency inference suitable for real-time closed-loop re-planning. We train exclusively on urban scenarios (real urban city streets, intersections and roundabouts of the city of Parma, Italy) collected from a 2D traffic simulator with reactive agents, and evaluate in closed-loop on both in-distribution and markedly out-of-distribution environments, including multi-lane highways and unseen urban scenarios. Our results show that the model generalizes reliably to these unseen conditions, maintaining stable closed-loop control and successfully completing scenarios that differ substantially from the training distribution. We attribute this to the BEV representation, which provides a geometry-centric view of the scene that is inherently less sensitive to distributional shifts, and to the flow-matching formulation, which learns a smooth vector field that degrades gracefully under distribution shift. We provide video demonstrations of closed-loop behavior at https://marcelloceresini.github.io/DirectControlFlowMatching.

Electrified chemical processes are incentivized by exposure to time-varying electricity markets to operate flexibly, but participating in demand response schemes can require satisfying terminal constraints over long horizons. Specifically, terminal constraints may be required when computing optimal schedules in order to preserve dynamic stability. Model-based optimization methods are computationally costly, and data-driven scheduling via reinforcement learning (RL) faces severe credit-assignment challenges. We integrate Goal-Space Planning (GSP) with Deep Deterministic Policy Gradient (DDPG), using learned temporally abstract models over discrete subgoals to propagate value across extended horizons. Using a simulated air separation benchmark, we demonstrate the proposed approach improves sample efficiency over standard DDPG while satisfying terminal storage constraints, mitigating myopic control behavior.

Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant values can achieve optimization effects, translating the process optimization problem into a process control problem. Currently, self-optimizing control is widely applied to steady-state optimization problems. However, the development of process systems exhibits a trend towards refinement, highlighting the importance of optimizing dynamic processes such as batch processes and grade transitions. This paper formally introduces the self-optimizing control problem for dynamic optimization, termed the dynamic self-optimizing control problem, extending the original definition of self-optimizing control. A novel concept, "dynamic controlled variables" (DCVs), is proposed, and an implicit control policy is presented based on this concept. The paper theoretically analyzes the advantages and generality of DCVs compared to explicit control strategies and elucidates the relationship between DCVs and traditional controllers. Moreover, this paper puts forth a data-driven approach to designing self-optimizing DCVs, which considers DCV design as a mapping identification problem and employs deep neural networks to parameterize the variables. Three case studies validate the efficacy and superiority of DCVs in approximating multi-valued and discontinuous functions, as well as their application to dynamic optimization problems with non-fixed horizons, which traditional self-optimizing control methods are unable to address.

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.

Pneumatically-actuated anthropomorphic robots with high degrees of freedom (DOF) offer significant potential for physical human-robot interaction. However, precise control of pneumatic actuators is challenging due to their inherent nonlinearities. This paper presents the development of a compact 13-DOF upper-body humanoid robot. To assess the feasibility of an effective controller, we first investigate its key dynamic properties, such as actuation time delays, and confirm that its behavior is reproducible across repeated trials. Leveraging this reproducibility, we implement a preliminary data-driven controller for a 4-DOF arm subsystem based on a multilayer perceptron with explicit time delay compensation. The network was trained on random movement data to generate pressure commands for tracking arbitrary trajectories. In comparative evaluations on this subsystem, the data-driven controller achieved lower tracking errors than a traditional PID controller. This result suggests that data-driven approaches are a promising option for controlling complex, high-DOF pneumatic robots.