Extremum Seeking Under Persistent Gradient Deception: A Switching Systems Approach

Galarza-Jimenez, Felipe; Poveda, Jorge I.; Bianchin, Gianluca; Dall’Anese, Emiliano

doi:10.1109/lcsys.2021.3050451

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…For unconstrained optimization problems, it has been shown in [22,Section 5.2] and [45] that switched ES algorithms are stable when each mode is stable and the switching is sufficiently slow. The novelty of Theorem 3 lies in the incorporation of constraints into the switched zeroth-order dynamics via projection maps.…”

Section: Switching Objective Functionsmentioning

confidence: 99%

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

Chen

Poveda

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This paper introduces a class of model-free feedback methods for solving generic constrained optimization problems where the specific mathematical forms of the objective and constraint functions are not available. The proposed methods, termed Projected Zeroth-Order (P-ZO) dynamics, incorporate projection maps into a class of continuous-time model-free dynamics that make use of periodic dithering for the purpose of gradient learning. In particular, the proposed P-ZO algorithms can be interpreted as new extremum-seeking algorithms that autonomously drive an unknown system toward a neighborhood of the set of solutions of an optimization problem using only output feedback, while systematically guaranteeing that the input trajectories remain in a feasible set for all times. In this way, the P-ZO algorithms can properly handle hard and asymptotical constraints in model-free optimization problems without using penalty terms or barrier functions. Moreover, the proposed dynamics have suitable robustness properties with respect to small bounded additive disturbances on the states and dynamics, a property that is fundamental for practical real-world implementations. Additional tracking results for time-varying and switching cost functions are also derived under stronger convexity and smoothness assumptions and using tools from hybrid dynamical systems. Numerical examples are presented throughout the paper to illustrate the above results.

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Section: Switching Objective Functionsmentioning

confidence: 99%

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

Chen

Poveda

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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“…4,5 In addition, the HJB (Hamilton-Jacobi-Bellman) equation for the switched system is a nonlinear difference or differential equation with multiple variables, and it is very difficult to obtain an analytical solution for solving such this equation. Although some methods have been proposed in the literature [6][7][8] to solve the optimal constrained control problem of the linear switched systems, these methods cannot be directly used to solve the optimal control problem of the nonlinear switched systems.…”

Section: Introductionmentioning

confidence: 99%

Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming

2023

Optim Control Appl Methods

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In this article, the zero‐sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve the Hamilton‐Jacobi‐Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. Finally, the validity of the method is verified by simulation examples.

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Resilient reinforcement learning and robust output regulation under denial-of-service attacks

Gao

Deng

et al. 2022

Automatica

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Extremum Seeking Under Persistent Gradient Deception: A Switching Systems Approach

Cited by 5 publications

References 22 publications

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

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

Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming

Resilient reinforcement learning and robust output regulation under denial-of-service attacks

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