arXiv subjects

Jorge I. Poveda

Publications and source records attributed to Jorge I. Poveda.

At least 37 records · Page 2Linked to original sources

arXiv2024

Hybrid Minimum-Seeking in Synergistic Lyapunov Functions: Robust Global Stabilization under Unknown Control Directions

We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global control Lyapunov functions. Building on a recently developed Lie-bracket averaging result for hybrid dynamic inclusions presented in \cite{abdelgalil2023lie}, we propose a novel class of universal hybrid feedback laws that achieve robust global practical stability by identifying the minimum point of a set of appropriately chosen synergistic Lyapunov functions. As concrete applications of our results, we synthesize different hybrid high-frequency high-amplitude feedback laws for the solution of robust global stabilization problems on various types of manifolds under unknown control directions, as well as controllers for obstacle avoidance problems in vehicles characterized by kinematic models describing both holonomic and non-holonomic models. By leveraging Lie-bracket averaging for hybrid systems, we also show how the proposed hybrid minimum-seeking feedback laws can overcome lack of controllability during persistent (bounded) periods of time. Numerical simulation results are presented to illustrate the main results.

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arXiv2024

Decentralized Concurrent Learning with Coordinated Momentum and Restart

This paper studies the stability and convergence properties of a class of multi-agent concurrent learning (CL) algorithms with momentum and restart. Such algorithms can be integrated as part of the estimation pipelines of data-enabled multi-agent control systems to enhance transient performance while maintaining stability guarantees. However, characterizing restarting policies that yield stable behaviors in decentralized CL systems, especially when the network topology of the communication graph is directed, has remained an open problem. In this paper, we provide an answer to this problem by synergistically leveraging tools from graph theory and hybrid dynamical systems theory. Specifically, we show that under a cooperative richness condition on the overall multi-agent system's data, and by employing coordinated periodic restart with a frequency that is tempered by the level of asymmetry of the communication graph, the resulting decentralized dynamics exhibit robust asymptotic stability properties, characterized in terms of input-to-state stability bounds, and also achieve a desirable transient performance. To demonstrate the practical implications of the theoretical findings, three applications are also presented: cooperative parameter estimation over networks with private data sets, cooperative model-reference adaptive control, and cooperative data-enabled feedback optimization of nonlinear plants.

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arXiv2023

Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness

We study the stability properties of a control system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with "sufficiently low frequency" in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.

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arXiv2023

Recurrent Neural Network ODE Output for Classification Problems Follows the Replicator Dynamics

This letter establishes a novel relationship between a class of recurrent neural networks and certain evolutionary dynamics that emerge in the context of population games. Specifically, it is shown that the output of a recurrent neural network, in the context of classification problems, coincides with the evolution of the population state in a population game. This connection is established with dynamic payoffs and under replicator evolutionary dynamics. The connection provides insights into the neural network's behavior from both dynamical systems and game-theoretical perspectives, aligning with recent literature that suggests that neural network outputs may resemble the Nash equilibria of suitable games. It also uncovers potential connections between the neural network classification problem and mechanism design. To illustrate our results, we present different numerical experiments in the context of classification problems.

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arXiv2023

Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions

We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that exhibit multiple time scales and are modeled by constrained differential inclusions, as well as discrete-time dynamics modeled by constrained difference inclusions with random inputs. By assuming regularity and causality of the dynamics and their solutions, respectively, we propose a suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster functions that can certify stability and recurrence using simpler functions related to the slow and fast dynamics of the system. We establish the stability properties with respect to compact sets, while the recurrence properties are studied only for open sets.

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arXiv2023

Prescribed-Time Control in Switching Systems with Resets: A Hybrid Dynamical Systems Approach

We consider the problem of achieving prescribed-time stability (PT-S) in a class of hybrid dynamical systems that incorporate switching nonlinear dynamics, exogenous inputs, and resets. By "prescribed-time stability", we refer to the property of having the states converge to a particular compact set of interest before a given time defined a priori by the user. We focus on dynamical systems that achieve this property via time-varying gains. For continuous-time systems, this approach has received significant attention in recent years, with various applications in control, optimization, and estimation problems. However, its extensions beyond continuous-time systems have been limited. This gap motivates this paper, which introduces a novel class of switching conditions for switching systems with resets that incorporate time-varying gains, ensuring the PT-S property even in the presence of unstable modes. The analysis leverages tools from hybrid dynamical system's theory, and a contraction-dilation property that is established for the hybrid time domains of the solutions of the system. We present the model and main results in a general framework and subsequently apply them to three novel applications: (a) PT regulation of switching plants with no common Lyapunov functions; (b) PT control of dynamic plants with uncertainty and intermittent feedback; and (c) PT decision-making in non-cooperative switching games via hybrid Nash seeking dynamics.

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arXiv2022

Momentum-Based Nash Set Seeking over Networks via Multi-Time Scale Hybrid Dynamic Inclusions

Multi-time scale techniques, such as singular perturbations and averaging theory, have played an essential role in the development of distributed Nash equilibrium-seeking algorithms for network systems. Such techniques intrinsically rely on the uniform asymptotic stability properties of the dynamics that evolve in each time scale of the closed-loop system. When such properties are absent, synthesizing multi-time scale Nash equilibrium-seeking algorithms is more challenging and requires additional regularization mechanisms. In this paper, we investigate the synthesis and analysis of these mechanisms in the context of accelerated pseudogradient flows with time-varying damping in non-cooperative games. Specifically, we introduce a new class of distributed and hybrid Nash set-seeking (NSS) algorithms that synergistically combine dynamic momentum-based flows with coordinated discrete-time resets. The reset mechanisms can be seen as restarting techniques that allow individual players to choose their own momentum restarting policy to achieve better transient performance. The resulting closed-loop system is modeled as a hybrid dynamic inclusion, which is analyzed using tools from hybrid dynamical system's theory. Our algorithms are developed for potential games, as well as for monotone games for which a potential function does not exist. They can be implemented in games where players have access to gradient Oracles with full or partial information, as well as in games where players have access only to measurements of their costs. In the latter case, we use tools from hybrid extremum seeking control to achieve accelerated model-free Nash set seeking.

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arXiv2022

Model-Free Optimization on Smooth Compact Manifolds: Overcoming Topological Obstructions using Zeroth-Order Hybrid Dynamics

Smooth autonomous dynamical systems modeled by ordinary differential equations (ODEs) cannot robustly and globally stabilize a point in compact, boundaryless manifolds. This obstruction, which is topological in nature, implies that traditional smooth optimization dynamics are not able to robustly solve global optimization problems in such spaces. In turn, model-free optimization algorithms, which usually inherit their stability and convergence properties from their model-based counterparts, might also suffer from similar topological obstructions. For example, this is the case in zeroth-order methods and perturbation-based techniques, where gradients and Hessians are usually estimated in real time via measurements or evaluations of the cost function. To address this issue, we introduce a class of hybrid model-free optimization dynamics that combine continuous-time and discrete-time feedback to overcome the obstructions that emerge in traditional ODE-based optimization algorithms evolving on smooth compact manifolds. In particular, we introduce a hybrid controller that switches between different model-free feedback-laws obtained by applying suitable exploratory geodesic dithers to a family of synergistic diffeomorphisms adapted to the cost function that defines the optimization problem. The geodesic dithers enable exploration of the manifold while preserving its forward invariance, a property that is important for many practical applications where physics-based constraints limit the feasible trajectories of the system. The hybrid controller exploits the information obtained from the geodesic dithers to achieve robust global practical stability of the set of minimizers of the cost. The proposed method is of model-free nature since it only requires measurements or evaluations of the cost function. Numerical results are presented to illustrate the main ideas and advantages of the method.

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arXiv2022

Data-Assisted Vision-Based Hybrid Control for Robust Stabilization with Obstacle Avoidance via Learning of Perception Maps

We study the problem of target stabilization with robust obstacle avoidance in robots and vehicles that have access only to vision-based sensors for the purpose of realtime localization. This problem is particularly challenging due to the topological obstructions induced by the obstacle, which preclude the existence of smooth feedback controllers able to achieve simultaneous stabilization and robust obstacle avoidance. To overcome this issue, we develop a vision-based hybrid controller that switches between two different feedback laws depending on the current position of the vehicle using a hysteresis mechanism and a data-assisted supervisor. The main innovation of the paper is the incorporation of suitable perception maps into the hybrid controller. These maps can be learned from data obtained from cameras in the vehicles and trained via convolutional neural networks (CNN). Under suitable assumptions on this perception map, we establish theoretical guarantees for the trajectories of the vehicle in terms of convergence and obstacle avoidance. Moreover, the proposed vision-based hybrid controller is numerically tested under different scenarios, including noisy data, sensors with failures, and cameras with occlusions.

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arXiv2022

Model-Free Feedback Constrained Optimization Via Projected Primal-Dual Zeroth-Order Dynamics

In this paper, we propose a model-free feedback solution method to solve generic constrained optimization problems, without knowing the specific formulations of the objective and constraint functions. This solution method is termed projected primal-dual zeroth-order dynamics (P-PDZD) and is developed based on projected primal-dual gradient dynamics and extremum seeking control. In particular, the P-PDZD method can be interpreted as a model-free controller that autonomously drives an unknown system to the solution of the optimization problem using only output feedback. The P-PDZD can properly handle both the hard and asymptotic constraints, and we develop the decentralized version of P-PDZD when applied to multi-agent systems. Moreover, we prove that the P-PDZD achieves semi-global practical asymptotic stability and structural robustness. We then apply the decentralized P-PDZD to the optimal voltage control problem in power distribution systems with square probing signals, and the simulation results verified the optimality, robustness, and adaptivity of the P-PDZD method.

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arXiv2022

Accelerated Continuous-Time Approximate Dynamic Programming via Data-Assisted Hybrid Control

We introduce a new closed-loop architecture for the online solution of approximate optimal control problems in the context of continuous-time systems. Specifically, we introduce the first algorithm that incorporates dynamic momentum in actor-critic structures to control continuous-time dynamic plants with an affine structure in the input. By incorporating dynamic momentum in our algorithm, we are able to accelerate the convergence properties of the closed-loop system, achieving superior transient performance compared to traditional gradient-descent based techniques. In addition, by leveraging the existence of past recorded data with sufficiently rich information properties, we dispense with the persistence of excitation condition traditionally imposed on the regressors of the critic and the actor. Given that our continuous-time momentum-based dynamics also incorporate periodic discrete-time resets that emulate restarting techniques used in the machine learning literature, we leverage tools from hybrid dynamical systems theory to establish asymptotic stability properties for the closed-loop system. We illustrate our results with a numerical example.

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arXiv2022

High-Performance Optimal Incentive-Seeking in Transactive Control for Traffic Congestion

Traffic congestion has dire economic and social impacts in modern metropolitan areas. To address this problem, in this paper we introduce a novel type of model-free transactive controllers to manage vehicle traffic in highway networks for which precise mathematical models are not available. Specifically, we consider a highway system with managed lanes on which dynamic tolling mechanisms can be implemented in real-time using measurements from the roads. We present three incentive-seeking feedback controllers able to find in real-time the optimal economic incentives (e.g., tolls) that persuade highway users to follow a suitable driving behavior that minimizes a predefined performance index. The controllers are agnostic with respect to the exact model of the highway, and they are also able to guarantee fast convergence to the optimal tolls by leveraging non-smooth and hybrid dynamic mechanisms that combine continuous-time dynamics and discrete-time dynamics. We provide numerical examples to illustrate the advantages of the different presented techniques.

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arXiv2022

A Stochastic Binary Vertex-Triggering Resetting Algorithm for Global Synchronization of Pulse-Coupled Oscillators

In this paper, we propose a novel stochastic binary resetting algorithm for networks of pulse-coupled oscillators (or, simply, agents) to reach global synchronization. The algorithm is simple to state: Every agent in a network oscillates at a common frequency. Upon completing an oscillation, an agent generates a Bernoulli random variable to decide whether it sends pulses to all of its out-neighbors or it stays quiet. Upon receiving a pulse, an agent resets its state by following a binary phase update rule. We show that such an algorithm can guarantee global synchronization of the agents almost surely as long as the underlying information flow topology is a rooted directed graph. The proof of the result relies on the use of a stochastic hybrid dynamical system approach. Toward the end of the paper, we present numerical demonstrations for the validity of the result and, also, numerical studies about the times needed to reach synchronization for various information flow topologies.

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arXiv2022

Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows

This paper studies the design of feedback controllers to steer a switching linear time-invariant dynamical system towards the solution trajectory of a time-varying convex optimization problem. We propose two types of controllers: (i) a continuous controller inspired by the online gradient descent method, and (ii) a hybrid controller that can be interpreted as an online version of Nesterov's accelerated gradient method with restarts of the state variables. By design, the controllers continuously steer the system towards the time-varying optimizer without requiring knowledge of exogenous disturbances affecting the system. For cost functions that are smooth and satisfy the Polyak-Łojasiewicz inequality, we demonstrate that the online gradient-flow controller ensures uniform global exponential stability when the time scales of the system and controller are sufficiently separated and the switching signal of the system varies slowly on average. For cost functions that are strongly convex, we show that the hybrid accelerated controller outperforms the continuous gradient descent method. When the cost function is not strongly convex, we show that the the hybrid accelerated method guarantees global practical asymptotic stability.

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arXiv2021

Planning a Return to Normal after the COVID-19 Pandemic: Identifying Safe Contact Levels via Online Optimization

Since the early months of 2020, non-pharmaceutical interventions (NPIs) -- implemented at varying levels of severity and based on widely-divergent perspectives of risk tolerance -- have been the primary means to control SARS-CoV-2 transmission. We seek to identify how risk tolerance and vaccination rates impact the rate at which a population can return to pre-pandemic contact behavior. To this end, we develop a novel feedback control method for data-driven decision-making to identify optimal levels of NPIs across geographical regions in order to guarantee that hospitalizations will not exceed a given risk tolerance. Results are shown for the state of Colorado, and they suggest that: coordination in decision-making across regions is essential to maintain the daily number of hospitalizations below the desired limits; increasing risk tolerance can decrease the number of days required to discontinue NPIs, at the cost of an increased number of deaths; and if vaccination uptake is less than 70\%, at most levels of risk tolerance, return to pre-pandemic contact behaviors before the early months of 2022 may newly jeopardize the healthcare system.

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arXiv2021

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the saddle-flow dynamics, modified to take into account projections on constraint sets and output-feedback from the plant. We derive sufficient conditions on the tunable parameters of the controller (inherently related to the time-scale separation between plant and controller dynamics) to guarantee exponential and input-to-state stability of the closed-loop system. The analysis is tailored to the case of time-varying strongly convex cost functions and polytopic output constraints. The theoretical results are further validated in a ramp metering control problem in a network of traffic highways.

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arXiv2021

Model-Free Optimal Voltage Control via Continuous-Time Zeroth-Order Methods

In power distribution systems, the growing penetration of renewable energy resources brings new challenges to maintaining voltage safety, which is further complicated by the limited model information of distribution systems. To address these challenges, we develop a model-free optimal voltage control algorithm based on projected primal-dual gradient dynamics and continuous-time zeroth-order method (extreme seeking control). This proposed algorithm i) operates purely based on voltage measurements and does not require any other model information, ii) can drive the voltage magnitudes back to the acceptable range, iii) satisfies the power capacity constraints all the time, iv) minimizes the total operating cost, and v) is implemented in a decentralized fashion where the privacy of controllable devices is preserved and plug-and-play operation is enabled. We prove that the proposed algorithm is semi-globally practically asymptotically stable and is structurally robust to measurement noises. Lastly, the performance of the proposed algorithm is further demonstrated via numerical simulations.

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arXiv2020

Fixed-Time Newton-Like Extremum Seeking

In this paper, we present a novel Newton-based extremum seeking controller for the solution of multivariable model-free optimization problems in static maps. Unlike existing asymptotic and fixed-time results in the literature, we present a scheme that achieves (practical) fixed time convergence to a neighborhood of the optimal point, with a convergence time that is independent of the initial conditions and the Hessian of the cost function, and therefore can be arbitrarily assigned a priori by the designer via an appropriate choice of parameters in the algorithm. The extremum seeking dynamics exploit a class of fixed time convergence properties recently established in the literature for a family of Newton flows, as well as averaging results for perturbed dynamical systems that are not necessarily Lipschitz continuous. The proposed extremum seeking algorithm is model-free and does not require any explicit knowledge of the gradient and Hessian of the cost function. Instead, real-time optimization with fixed-time convergence is achieved by using real time measurements of the cost, which is perturbed by a suitable class of periodic excitation signals generated by a dynamic oscillator. Numerical examples illustrate the performance of the algorithm.

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