arXiv subjects

Hamidreza Modares

Publications and source records attributed to Hamidreza Modares.

At least 19 recordsLinked to original sources

arXiv2026

Direct Data Driven Natural Gradient Descent for Control

This paper introduces a novel direct data-driven control framework based on Natural Gradient Descent (NGD) to design interpretable and robust closed-loop policies without requiring explicit model identification. We propose two data-driven NGD formulations that incorporate the closed-loop covariance matrix through the Fisher Information Matrix (FIM), allowing gradient updates to be preconditioned according to the system's intrinsic uncertainty. Leveraging two distinct data-based parameterizations of the closed-loop system, our method enables stability-guaranteed policy synthesis directly from data. We provide theoretical guarantees for contraction and convergence using semidefinite programs (SDPs) and validate our framework in both simulations and on hardware on a ROSbot XL platform. The results demonstrate intuitive features compared to linear-quadratic regulator (LQR) and standard data-driven baselines, particularly in terms of convergence speed, robustness, and control interpretability. This work bridges the gap between trajectory-oriented natural gradient methods and practical data-driven control design.

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arXiv2026

Reachability Analysis With Probabilistic Zonotopes: Learning Realized Disturbances and Refining Aleatory Uncertainty

This paper develops a data-driven reachability framework for linear systems whose disturbances are modeled by probabilistic zonotopes (PZs), combining bounded deterministic and Gaussian stochastic components. In contrast to methods that require a precisely known disturbance model (either purely deterministic or purely stochastic), we assume only a conservative prior PZ and refine it from data. The framework separates two uncertainty sources: realized disturbances, which act along the collected trajectory and govern the size of the data-consistent model set, and aleatory disturbances, which enter as future additive uncertainty during reachable-set propagation; both shape the reachable sets, but through different mechanisms. Refinement exploits prior system knowledge together with trajectory-consistency constraints induced by the data, which impose affine couplings between deterministic and Gaussian latent variables. We accordingly develop a constrained-PZ calculus that absorbs the stochastic part of these constraints into an equivalent representation, removes infeasible latent directions, and reduces stochastic covariance, together with identification-aware fusion rules for combining heterogeneous constrained-PZ descriptions. The refined realized-disturbance proxies then serve as scenarios in a linear program that learns the smallest translated and scaled copy of the prior disturbance set that contains all proxy confidence sets while remaining nested in the prior. The resulting deterministic, high-probability reachable sets carry formal containment guarantees with substantially reduced conservatism, and numerical examples confirm that the pipeline tightens both the data-consistent model set and the propagated reachable sets.

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arXiv2026

Data-based Low-conservative Nonlinear Safe Control Learning

This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables controller synthesis and safety certification directly from data. Unlike existing methods that treat unmodeled nonlinearities as global worst-case uncertainties using Lipschitz bounds, the proposed approach embeds nonlinear terms directly into the invariance conditions via a geometry-aware difference-of-convex formulation. This enables facet- and direction-specific convexification, avoiding both nonlinearity cancellation and the excessive conservatism induced by uniform global bounds. We further propose a vertex-dependent controller construction that enforces convexity and contractivity conditions locally on the active facets associated with each vertex, thereby enlarging the class of certifiable invariant sets. For systems subject to additive disturbances, disturbance effects are embedded directly into the verification conditions through optimized, geometry-dependent bounds, rather than via uniform margin inflation, yielding less conservative robust safety guarantees. As a result, the proposed methods can certify substantially larger safe sets, naturally accommodate joint state and input constraints, and provide data-driven safety guarantees. The simulation results show a significant improvement in both nonlinearity tolerance and the size of the certified safe set.

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arXiv2025

Safe Navigation with Zonotopic Tubes: An Elastic Tube-based MPC Framework

This paper presents an elastic tube-based model predictive control (MPC) framework for unknown discrete-time linear systems subject to disturbances. Unlike most existing elastic tube-based MPC methods, we do not assume perfect knowledge of the system model or disturbance realizations bounds. Instead, a conservative zonotopic disturbance set is initialized and iteratively refined using data and prior knowledge: data are used to identify matrix zonotope model sets for the system dynamics, while prior physical knowledge is employed to discard models and disturbances inconsistent with known constraints. This process yields constrained matrix zonotopes representing disturbance realizations and dynamics that enable a principled fusion of offline information with limited online data, improving MPC feasibility and performance. The proposed design leverages closed-loop system characterization to learn and refine control gains that maintain a small tube size. By separating open-loop model mismatch from closed-loop effects in the error dynamics, the method avoids dependence on the size of the state and input operating regions, thereby reducing conservatism. An adaptive co-design of the tube and ancillary feedback ensures $\lambda$-contractive zonotopic tubes, guaranteeing robust positive invariance, improved feasibility margins, and enhanced disturbance tolerance. We establish recursive feasibility conditions and introduce a polyhedral Lyapunov candidate for the error tube, proving exponential stability of the closed-loop error dynamics under the adaptive tube-gain updates. Simulations demonstrate improved robustness, enlarged feasibility regions, and safe closed-loop performance using only a small amount of online data.

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arXiv2025

Robust Model Predictive Control Design for Autonomous Vehicles with Perception-based Observers

This paper presents a robust model predictive control (MPC) framework that explicitly addresses the non-Gaussian noise inherent in deep learning-based perception modules used for state estimation. Recognizing that accurate uncertainty quantification of the perception module is essential for safe feedback control, our approach departs from the conventional assumption of zero-mean noise quantification of the perception error. Instead, it employs set-based state estimation with constrained zonotopes to capture biased, heavy-tailed uncertainties while maintaining bounded estimation errors. To improve computational efficiency, the robust MPC is reformulated as a linear program (LP), using a Minkowski-Lyapunov-based cost function with an added slack variable to prevent degenerate solutions. Closed-loop stability is ensured through Minkowski-Lyapunov inequalities and contractive zonotopic invariant sets. The largest stabilizing terminal set and its corresponding feedback gain are then derived via an ellipsoidal approximation of the zonotopes. The proposed framework is validated through both simulations and hardware experiments on an omnidirectional mobile robot along with a camera and a convolutional neural network-based perception module implemented within a ROS2 framework. The results demonstrate that the perception-aware MPC provides stable and accurate control performance under heavy-tailed noise conditions, significantly outperforming traditional Gaussian-noise-based designs in terms of both state estimation error bounding and overall control performance.

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arXiv2025

SAFE--MA--RRT: Multi-Agent Motion Planning with Data-Driven Safety Certificates

This paper proposes a fully data-driven motion-planning framework for homogeneous linear multi-agent systems that operate in shared, obstacle-filled workspaces without access to explicit system models. Each agent independently learns its closed-loop behavior from experimental data by solving convex semidefinite programs that generate locally invariant ellipsoids and corresponding state-feedback gains. These ellipsoids, centered along grid-based waypoints, certify the dynamic feasibility of short-range transitions and define safe regions of operation. A sampling-based planner constructs a tree of such waypoints, where transitions are allowed only when adjacent ellipsoids overlap, ensuring invariant-to-invariant transitions and continuous safety. All agents expand their trees simultaneously and are coordinated through a space-time reservation table that guarantees inter-agent safety by preventing simultaneous occupancy and head-on collisions. Each successful edge in the tree is equipped with its own local controller, enabling execution without re-solving optimization problems at runtime. The resulting trajectories are not only dynamically feasible but also provably safe with respect to both environmental constraints and inter-agent collisions. Simulation results demonstrate the effectiveness of the approach in synthesizing synchronized, safe trajectories for multiple agents under shared dynamics and constraints, using only data and convex optimization tools.

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arXiv2025

Data-Driven Motion Planning for Uncertain Nonlinear Systems

This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and solves data-driven linear-matrix-inequality problems to learn several ellipsoidal invariant sets together with their local state-feedback gains. The convex hull of these ellipsoids, still invariant under a piece-wise-affine controller obtained by interpolating the gains, is then approximated by a polytope. Safe transitions between nodes are ensured by verifying the intersection of consecutive convex-hull polytopes and introducing an intermediate node for a smooth transition. Control gains are interpolated in real time via simplex-based interpolation, keeping the state inside the invariant polytopes throughout the motion. Unlike traditional approaches that rely on system dynamics models, our method requires only data to compute safe regions and design state-feedback controllers. The approach is validated through simulations, demonstrating the effectiveness of the proposed method in achieving safe, dynamically feasible paths for complex nonlinear systems.

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arXiv2025

Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems

This paper presents a risk-aware safe reinforcement learning (RL) control design for stochastic discrete-time linear systems. Rather than using a safety certifier to myopically intervene with the RL controller, a risk-informed safe controller is also learned besides the RL controller, and the RL and safe controllers are combined together. Several advantages come along with this approach: 1) High-confidence safety can be certified without relying on a high-fidelity system model and using limited data available, 2) Myopic interventions and convergence to an undesired equilibrium can be avoided by deciding on the contribution of two stabilizing controllers, and 3) highly efficient and computationally tractable solutions can be provided by optimizing over a scalar decision variable and linear programming polyhedral sets. To learn safe controllers with a large invariant set, piecewise affine controllers are learned instead of linear controllers. To this end, the closed-loop system is first represented using collected data, a decision variable, and noise. The effect of the decision variable on the variance of the safe violation of the closed-loop system is formalized. The decision variable is then designed such that the probability of safety violation for the learned closed-loop system is minimized. It is shown that this control-oriented approach reduces the data requirements and can also reduce the variance of safety violations. Finally, to integrate the safe and RL controllers, a new data-driven interpolation technique is introduced. This method aims to maintain the RL agent's optimal implementation while ensuring its safety within environments characterized by noise. The study concludes with a simulation example that serves to validate the theoretical results.

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arXiv2025

Non-Conservative Data-driven Safe Control Design for Nonlinear Systems with Polyhedral Safe Sets

This paper presents a data-driven nonlinear safe control design approach for discrete-time systems under parametric uncertainties and additive disturbances. We first characterize a new control structure from which a data-based representation of closed-loop systems is obtained. This data-based closed-loop system is composed of two parts: 1) a parametrized linear closed-loop part and a parametrized nonlinear remainder closed-loop part. We show that using the standard practice or learning a robust controller to ensure safety while treating the remaining nonlinearities as disturbances brings about significant challenges in terms of computational complexity and conservatism. To overcome these challenges, we develop a novel nonlinear safe control design approach in which the closed-loop nonlinear remainders are learned, rather than canceled, in a control-oriented fashion while preserving the computational efficiency. To this end, a primal-dual optimization framework is leveraged in which the control gains are learned to enforce the second-order optimality on the closed-loop nonlinear remainders. This allows us to account for nonlinearities in the design for the sake of safety rather than treating them as disturbances. This new controller parameterization and design approach reduces the computational complexity and the conservatism of designing a safe nonlinear controller. A simulation example is then provided to show the effectiveness of the proposed data-driven controller.

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arXiv2025

Direct Data Driven Control Using Noisy Measurements

This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems -- including a rotary inverted pendulum and an active suspension system -- demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible.

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arXiv2025

Unifying Direct and Indirect Learning for Safe Control of Linear Systems

This paper develops learning-enabled safe controllers for linear systems subject to system uncertainties and bounded disturbances. Given the disturbance zonotope, the databased closed-loop dynamics (CLDs) are first characterized using a matrix zonotope (MZ), and refined through several steps to yield a constrained matrix zonotope (CMZ). This refinement is achieved by introducing conformal equality constraints that eliminate incompatible disturbance realizations. More precisely, prior knowledge and observed data are used separately to construct CMZ representations of disturbance sequences that conform to both data and prior knowledge, and are intersected by the initial MZ of the disturbance sequence, producing a refined CMZ. This approach reduces conservatism. To further reduce the conservativeness, we unify open-loop learning with closed-loop learning by presenting a novel set-membership identification method that models open-loop dynamics as a CMZ. The prior knowledge serves as an initial feasible open-loop model set (FOLMS) of this CMZ, which is refined into a posterior set whenever new informative online data becomes available. This posterior FOLMS then adaptively replaces the prior knowledge set employed in the disturbance elimination of the closed-loop learning process. The resulting refined parameterized set of CLD is subsequently leveraged to directly and adaptively learn a controller that robustly enforces safety. Toward this goal, we formulate a linear programming problem that guarantees {\lambda}contractiveness of a polyhedral safe set. A simulation example is provided to validate the effectiveness of the proposed approach and support the theoretical results.

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arXiv2025

Natural Gradient Descent for Control

This paper bridges optimization and control, and presents a novel closed-loop control framework based on natural gradient descent, offering a trajectory-oriented alternative to traditional cost-function tuning. By leveraging the Fisher Information Matrix, we formulate a preconditioned gradient descent update that explicitly shapes system trajectories. We show that, in sharp contrast to traditional controllers, our approach provides flexibility to shape the system's low-level behavior. To this end, the proposed method parameterizes closed-loop dynamics in terms of stationary covariance and an unknown cost function, providing a geometric interpretation of control adjustments. We establish theoretical stability conditions. The simulation results on a rotary inverted pendulum benchmark highlight the advantages of natural gradient descent in trajectory shaping.

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arXiv2025

Integration of Prior Knowledge into Direct Learning for Safe Control of Linear Systems

This paper integrates prior knowledge into direct learning of safe controllers for linear uncertain systems under disturbances. To this end, we characterize the set of all closed-loop systems that can be explained by available prior knowledge of the system model and the disturbances. We leverage matrix zonotopes for data-based characterization of closed-loop systems and show that the explainability of closed-loop systems by prior knowledge can be formalized by adding an equality conformity constraint to the matrix zonotope. We then leverage the resulting constraint matrix zonotope and design safe controllers that conform with both data and prior knowledge. This is achieved by ensuring the inclusion of a constrained zonotope of all possible next states in a {\lambda}-scaled level set of the safe set. We consider both polytope and zonotope safe sets and provide set inclusion conditions using linear programming.

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arXiv2024

Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach

In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value matrix of the Lyapunov cost function. This formulation provides a new framework for analyzing and designing feedback control laws. We show that any stable closed-loop system can be expressed in this form with appropriate values for the step size and value matrices. Furthermore, we show that this parameterization of the closed-loop system is equivalent to a linear quadratic regulator for appropriately chosen weighting matrices. We also show that trajectories can be shaped using this approach to achieve a desired closed-loop behavior.

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arXiv2024

Direct Data-Driven Discounted Infinite Horizon Linear Quadratic Regulator with Robustness Guarantees

This paper presents a one-shot learning approach with performance and robustness guarantees for the linear quadratic regulator (LQR) control of stochastic linear systems. Even though data-based LQR control has been widely considered, existing results suffer either from data hungriness due to the inherently iterative nature of the optimization formulation (e.g., value learning or policy gradient reinforcement learning algorithms) or from a lack of robustness guarantees in one-shot non-iterative algorithms. To avoid data hungriness while ensuing robustness guarantees, an adaptive dynamic programming formalization of the LQR is presented that relies on solving a Bellman inequality. The control gain and the value function are directly learned by using a control-oriented approach that characterizes the closed-loop system using data and a decision variable from which the control is obtained. This closed-loop characterization is noise-dependent. The effect of the closed-loop system noise on the Bellman inequality is considered to ensure both robust stability and suboptimal performance despite ignoring the measurement noise. To ensure robust stability, it is shown that this system characterization leads to a closed-loop system with multiplicative and additive noise, enabling the application of distributional robust control techniques. The analysis of the suboptimality gap reveals that robustness can be achieved without the need for regularization or parameter tuning. The simulation results on the active car suspension problem demonstrate the superiority of the proposed method in terms of robustness and performance gap compared to existing methods.

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arXiv2022

Finite-time Koopman Identifier: A Unified Batch-online Learning Framework for Joint Learning of Koopman Structure and Parameters

In this paper, a unified batch-online learning approach is introduced to learn a linear representation of nonlinear system dynamics using the Koopman operator. The presented system modeling approach leverages a novel incremental Koopman-based update law that retrieves a mini-batch of samples stored in a memory to not only minimizes the instantaneous Koopman operator's identification errors but also the identification errors for the batch of retrieved samples. Discontinuous modifications of gradient flows are presented for the online update law to assure finite-time convergence under easy-to-verify conditions defined on the batch of data. Therefore, this unified online-batch framework allows performing joint sample- and time-domain analysis for converging the Koopman operator's parameters. More specifically, it is shown that if the collected mini-batch of samples guarantees a rank condition, then finite-time guarantee in the time domain can be certified and the settling time depends on the quality of collected samples being reused in the update law. Moreover, the efficiency of the proposed Koopman-based update law is further analyzed by showing that the identification regret in continuous time grows sub-linearly with time. Furthermore, to avoid learning corrupted dynamics due to the selection of an inappropriate set of Koopman observables, a higher-layer meta learner employs a discrete Bayesian optimization algorithm to obtain the best library of observable functions for the operator. Since finite-time convergence of the Koopman model for each set of observable is guaranteed under a rank condition on stored data, the fitness of each set of observables can be obtained based on the identification error on the stored samples in the proposed framework and even without implementing any controller based on the learned system.

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arXiv2022

Data-driven Safe Control of Linear Systems Under Epistemic and Aleatory Uncertainties

Safe control of constrained linear systems under both epistemic and aleatory uncertainties is considered. The aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF) and the epistemic uncertainty characterizes the lack of knowledge on the system dynamics. Data-based probabilistic safe controllers are designed for the cases where the noise PDF is 1) zero-mean Gaussian with a known covariance, 2) zero-mean Gaussian with an uncertain covariance, and 3) zero-mean non-Gaussian with an unknown distribution. Easy-to-check model-based conditions for guaranteeing probabilistic safety are provided for the first case by introducing probabilistic contractive sets. These results are then extended to the second and third cases by leveraging distributionally-robust probabilistic safe control and conditional value-at-risk (CVaR) based probabilistic safe control, respectively. Data-based implementations of these probabilistic safe controllers are then considered. It is shown that data-richness requirements for directly learning a safe controller is considerably weaker than data-richness requirements for model-based safe control approaches that undertake a model identification. Moreover, an upper bound on the minimal risk level, under which the existence of a safe controller is guaranteed, is learned using collected data. A simulation example is provided to show the effectiveness of the proposed approach.

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arXiv2022

A Risk-Averse Preview-based $Q$-Learning Algorithm: Application to Highway Driving of Autonomous Vehicles

A risk-averse preview-based $Q$-learning planner is presented for navigation of autonomous vehicles. To this end, the multi-lane road ahead of a vehicle is represented by a finite-state non-stationary Markov decision process (MDP). A risk assessment unit module is then presented that leverages the preview information provided by sensors along with a stochastic reachability module to assign reward values to the MDP states and update them as scenarios develop. A sampling-based risk-averse preview-based Q-learning algorithm is finally developed that generates samples using the preview information and reward function to learn risk-averse optimal planning strategies without actual interaction with the environment. The risk factor is imposed on the objective function to avoid fluctuation of the Q values, which can jeopardize the vehicle's safety and/or performance. The overall hybrid automaton model of the system is leveraged to develop a feasibility check unit module that detects unfeasible plans and enables the planner system to react proactively to the changes of the environment. Finally, to verify the efficiency of the presented algorithm, its implementation on two highway driving scenarios of an autonomous vehicle in a varying traffic density is considered.

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