arXiv subjects

Jorge Cortés

Publications and source records attributed to Jorge Cortés.

At least 37 records · Page 2Linked to original sources

arXiv2026

Visibility in Polygonal Environments with Holes: Finding Best Spots for Hiding and Surveillance

Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is unknown. We consider environments modeled as polygons with holes. We develop a set of mathematical tools for reasoning about visibility as a function of position and rely on non-smooth analysis to formally characterize the regularity properties of various visibility-based metrics. These metrics are non-smooth and non-convex, so off-the-shelf optimization algorithms can only guarantee convergence to Clarke critical points. To address this, the proposed Normalized Descent algorithm leverages the structure of non-smooth points in visibility problems and introduces randomness to escape saddle points. Our technical analysis allows for the non-monotonic decrease in the visibility metric and strengthens the algorithm guarantees, ensuring convergence to local minima with high probability. Simulations on two hide-and-seek scenarios showcase the effectiveness of the proposed approach.

math.OC↗

arXiv2026

Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions

Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict stepwise decrease in the Lyapunov function but such certificates are difficult to construct for learned policies. The RL value function is a natural candidate but it is not well understood how it can be adapted for this purpose. To gain intuition, we first study the linear quadratic regulator (LQR) problem and make two key observations. First, a Lyapunov function can be obtained from the value function of an LQR policy by augmenting it with a residual term related to the system dynamics and stage cost. Second, the classical Lyapunov decrease requirement can be relaxed to a generalized Lyapunov condition requiring only decrease on average over multiple time steps. Using this intuition, we consider the nonlinear setting and formulate an approach to learn generalized Lyapunov functions by augmenting RL value functions with neural network residual terms. Our approach successfully certifies the stability of RL policies trained on Gymnasium and DeepMind Control benchmarks. We also extend our method to jointly train neural controllers and stability certificates using a multi-step Lyapunov loss, resulting in larger certified inner approximations of the region of attraction compared to the classical Lyapunov approach. Overall, our formulation enables stability certification for a broad class of systems with learned policies by making certificates easier to construct, thereby bridging classical control theory and modern learning-based methods.

cs.LG↗

arXiv2026

Gradient sampling algorithm for subsmooth functions

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem, neither its values nor its gradients are available in closed form, which calls for approximation. Our approach hinges upon extending the so-called gradient sampling algorithm, which approximates the Clarke generalized gradient of the objective function at a point by sampling its derivative at nearby locations. This allows us to select descent directions around points where the function may fail to be differentiable and establish algorithm convergence to a stationary point from any initial condition. Our key contribution is to prove this convergence by alleviating the requirement on continuous differentiability of the objective function on an open set of full measure. We further provide assumptions under which a desired convex subset of the decision space is rendered attractive for the iterates of the algorithm.

math.OC↗

arXiv2025

Anytime Safe Reinforcement Learning

This paper considers the problem of solving constrained reinforcement learning problems with anytime guarantees, meaning that the algorithmic solution returns a safe policy regardless of when it is terminated. Drawing inspiration from anytime constrained optimization, we introduce Reinforcement Learning-based Safe Gradient Flow (RL-SGF), an on-policy algorithm which employs estimates of the value functions and their respective gradients associated with the objective and safety constraints for the current policy, and updates the policy parameters by solving a convex quadratically constrained quadratic program. We show that if the estimates are computed with a sufficiently large number of episodes (for which we provide an explicit bound), safe policies are updated to safe policies with a probability higher than a prescribed tolerance. We also show that iterates asymptotically converge to a neighborhood of a KKT point, whose size can be arbitrarily reduced by refining the estimates of the value function and their gradients. We illustrate the performance of RL-SGF in a navigation example.

eess.SY↗

arXiv2025

On the Exponential Stability of Koopman Model Predictive Control

Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic stability have been studied, explicit guarantees of local exponential stability seem to be missing. This paper revisits the exponential stability for Koopman MPC. We first analyze a Koopman LQR problem and show that 1) with zero modeling error, the lifted LQR policy is globally optimal and globally asymptotically stabilizes the nonlinear plant, and 2) with the lifting function and one-step prediction error both Lipschitz at the origin, the closed-loop system is locally exponentially stable. These results facilitate terminal cost/set design in the lifted Koopman space. Leveraging linear-MPC properties (boundedness, value decrease, recursive feasibility), we then prove local exponential stability for a stabilizing Koopman MPC under the same conditions as Koopman LQR. Experiments on an inverted pendulum show better convergence performance and lower accumulated cost than the traditional Taylor-linearized MPC approaches.

math.OC↗

arXiv2025

Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families

The Koopman operator, originally defined for dynamical systems without input, has inspired many applications in control. Yet, the theoretical foundations underpinning this progress in control remain underdeveloped. This paper investigates the theoretical structure and connections between two extensions of Koopman theory to control: (i) Koopman operator via infinite input sequences and (ii) the Koopman control family. Although these frameworks encode system information in fundamentally different ways, we show that under certain conditions on the function spaces they operate on, they are equivalent. The equivalence is both in terms of the actions of the Koopman-based formulations in each framework as well as the function values on the system trajectories. Our analysis provides constructive tools to translate between the frameworks, offering a unified perspective for Koopman methods in control.

math.OC↗

arXiv2025

Generalized Multi-Constraint Extremum Seeking

We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These constraints may represent safety or other critical conditions. The proposed ES algorithm functions as a general nonlinear programming tool, offering practical maintenance of all constraints and semiglobal practical asymptotic stability, utilizing a Lyapunov argument on the penalty function and the set-valued Lie derivative. The efficacy of the algorithm is demonstrated on a 2D problem.

math.OC↗

arXiv2025

Safe Event-triggered Gaussian Process Learning for Barrier-Constrained Control

While control barrier functions (CBFs) are employed in addressing safety, control synthesis methods based on them generally rely on accurate system dynamics. This is a critical limitation, since the dynamics of complex systems are often not fully known. Supervised machine learning techniques hold great promise for alleviating this weakness by inferring models from data. We propose a novel \revision{approach for safe event-triggered learning of Gaussian process models in CBF-based continuous-time control for unknown control-affine systems. By applying a finite excitation at triggering times, our approach ensures a sufficient information gain to maintain the feasibility of the CBF-based safety condition with high probability. Our approach probabilistically guarantees safety based on a suitable GP prior and rules out} Zeno behavior in the triggering scheme. The effectiveness of the proposed approach and theory is demonstrated in simulations.

eess.SY↗

arXiv2025

Data-Driven Stabilization of Unknown Linear-Threshold Network Dynamics

This paper studies the data-driven control of unknown linear-threshold network dynamics to stabilize the state to a reference value. We consider two types of controllers: (i) a state feedback controller with feed-forward reference input and (ii) an augmented feedback controller with error integration. The first controller features a simpler structure and is easier to design, while the second offers improved performance in the presence of system parameter changes and disturbances. Our design strategy employs state-input datasets to construct data-based representations of the closed-loop dynamics. Since these representations involve linear threshold functions, we rewrite them as switched linear systems, and formulate the design problem as that of finding a common controller for all the resulting modes. This gives rise to a set of linear matrix inequalities (LMIs) whose solutions corresponds to the controller gain matrices. We analyze the computational complexity of solving the LMIs and propose a simplified, sufficient set of conditions that scales linearly with the system state. Simulations on two case studies involving regulation of firing rate dynamics in rodent brains and of arousal level dynamics in humans demonstrate the effectiveness of the controller designs.

eess.SY↗

arXiv2025

Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow

This paper considers the problem of solving constrained reinforcement learning (RL) problems with anytime guarantees, meaning that the algorithmic solution must yield a constraint-satisfying policy at every iteration of its evolution. Our design is based on a discretization of the Robust Safe Gradient Flow (RSGF), a continuous-time dynamics for anytime constrained optimization whose forward invariance and stability properties we formally characterize. The proposed strategy, termed RSGF-RL, is an off-policy algorithm which uses episodic data to estimate the value functions and their gradients and updates the policy parameters by solving a convex quadratically constrained quadratic program. Our technical analysis combines statistical analysis, the theory of stochastic approximation, and convex analysis to determine the number of episodes sufficient to ensure that safe policies are updated to safe policies and to recover from an unsafe policy, both with an arbitrary user-specified probability, and to establish the asymptotic convergence to the set of KKT points of the RL problem almost surely. Simulations on a navigation example and the cart-pole system illustrate the superior performance of RSGF-RL with respect to the state of the art.

eess.SY↗

arXiv2025

From Space to Time: Enabling Adaptive Safety with Learned Value Functions via Disturbance Recasting

The widespread deployment of autonomous systems in safety-critical environments such as urban air mobility hinges on ensuring reliable, performant, and safe operation under varying environmental conditions. One such approach, value function-based safety filters, minimally modifies a nominal controller to ensure safety. Recent advances leverage offline learned value functions to scale these safety filters to high-dimensional systems. However, these methods assume detailed priors on all possible sources of model mismatch, in the form of disturbances in the environment -- information that is rarely available in real world settings. Even in well-mapped environments like urban canyons or industrial sites, drones encounter complex, spatially-varying disturbances arising from payload-drone interaction, turbulent airflow, and other environmental factors. We introduce SPACE2TIME, which enables safe and adaptive deployment of offline-learned safety filters under unknown, spatially-varying disturbances. The key idea is to reparameterize spatial variations in disturbance as temporal variations, enabling the use of precomputed value functions during online operation. We validate SPACE2TIME on a quadcopter through extensive simulations and hardware experiments, demonstrating significant improvement over baselines.

cs.RO↗

arXiv2025

Feedback Optimization with State Constraints through Control Barrier Functions

Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the growing literature on the topic, the important problem of enforcing state constraints at all times remains unaddressed. In this work, we present the first feedback-optimization method that enforces state constraints. The method combines a class of dynamics called safe gradient flows with high-order control barrier functions. We provide a number of results on our proposed controller, including well-posedness guarantees, anytime constraint-satisfaction guarantees, equivalence between the closed-loop's equilibria and the optimization problem's critical points, and local asymptotic stability of optima.

math.OC↗

arXiv2025

Polarized Emission of Intrabinary Shocks in Spider Pulsars from Global 3D Kinetic Simulations

In spider pulsar systems, a relativistic intrabinary shock forms when the pulsar wind collides with the massive outflow driven off the pulsar's low-mass stellar companion. The shock is a site of non-thermal particle acceleration, likely via shock-driven magnetic reconnection, and produces synchrotron emission. These shocks are among the few systems in which global scales can be reasonably captured with kinetic simulations, enabling first-principles particle acceleration and emission studies. We perform the first global 3D kinetic simulations of spider pulsar intrabinary shocks and predict their polarized emission properties. We report emission spectra, light curves, and polarization patterns as a function of the stripe-averaged magnetic field, cooling strength, and viewing inclination. At $90^\circ$ inclination and for a low stripe-averaged magnetic field, we reproduce the double peaked light curve observed in spider systems. We predict a significant polarization degree $\gtrsim15\%$, which monotonically increases with the stripe-averaged field strength. Our results can be applied to and tested by forthcoming X-ray polarization observations of spider pulsars.

astro-ph.HE↗

arXiv2025

Modeling Nonlinear Control Systems via Koopman Control Family: Universal Forms and Subspace Invariance Proximity

This paper introduces the Koopman Control Family (KCF), a mathematical framework for modeling general (not necessarily control-affine) discrete-time nonlinear control systems with the aim of providing a solid theoretical foundation for the use of Koopman-based methods in systems with inputs. We demonstrate that the concept of KCF captures the behavior of nonlinear control systems on a (potentially infinite-dimensional) function space. By employing a generalized notion of subspace invariance under the KCF, we establish a universal form for finite-dimensional models, which encompasses the commonly used linear, bilinear, and linear switched models as specific instances. In cases where the subspace is not invariant under the KCF, we propose a method for approximating models in general form and characterize the model's accuracy using the concept of invariance proximity. We end by discussing how the proposed framework naturally lends itself to data-driven modeling of control systems.

math.OC↗

arXiv2025

Stability Constrained Voltage Control in Distribution Grids with Arbitrary Communication Infrastructure

We consider the problem of designing learning-based reactive power controllers that perform voltage regulation in distribution grids while ensuring closed-loop system stability. In contrast to existing methods, where the provably stable controllers are restricted to be decentralized, we propose a unified design framework that enables the controllers to take advantage of an arbitrary communication infrastructure on top of the physical power network. This allows the controllers to incorporate information beyond their local bus, covering existing methods as a special case and leading to less conservative constraints on the controller design. We then provide a design procedure to construct input convex neural network (ICNN) based controllers that satisfy the identified stability constraints by design under arbitrary communication scenarios, and train these controllers using supervised learning. Simulation results on the the University of California, San Diego (UCSD) microgrid testbed illustrate the effectiveness of the framework and highlight the role of communication in improving control performance.

eess.SY↗

arXiv2025

Data-driven stabilization of switched and constrained linear systems

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov-Metzler inequalities, we derive data-dependent bilinear programs whose solution directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for a perturbed linear system. We validate our theoretical findings numerically, demonstrating the favourable trade-off between conservatism and tractability achieved by the proposed relaxations.

math.OC↗

arXiv2025

Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filters

Designing controllers that accomplish tasks while guaranteeing safety constraints remains a significant challenge. We often want an agent to perform well in a nominal task, such as environment exploration, while ensuring it can avoid unsafe states and return to a desired target by a specific time. In particular we are motivated by the setting of safe, efficient, hands-off training for reinforcement learning in the real world. By enabling a robot to safely and autonomously reset to a desired region (e.g., charging stations) without human intervention, we can enhance efficiency and facilitate training. Safety filters, such as those based on control barrier functions, decouple safety from nominal control objectives and rigorously guarantee safety. Despite their success, constructing these functions for general nonlinear systems with control constraints and system uncertainties remains an open problem. This paper introduces a safety filter obtained from the value function associated with the reach-avoid problem. The proposed safety filter minimally modifies the nominal controller while avoiding unsafe regions and guiding the system back to the desired target set. By preserving policy performance while allowing safe resetting, we enable efficient hands-off reinforcement learning and advance the feasibility of safe training for real world robots. We demonstrate our approach using a modified version of soft actor-critic to safely train a swing-up task on a modified cartpole stabilization problem.

eess.SY↗

arXiv2025

Controller Design for Bilinear Neural Feedback Loops

This paper considers a class of bilinear systems with a neural network in the loop. These arise naturally when employing machine learning techniques to approximate general, non-affine in the input, control systems. We propose a controller design framework that combines linear fractional representations and tools from linear parameter varying control to guarantee local exponential stability of a desired equilibrium. The controller is obtained from the solution of linear matrix inequalities, which can be solved offline, making the approach suitable for online applications. The proposed methodology offers tools for stability and robustness analysis of deep neural networks interconnected with dynamical systems.

eess.SY↗