Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach

TL;DR

This paper introduces a game-theoretic, physics-informed machine learning framework for achieving robust, optimal, and safe predefined-time stabilization of nonlinear systems under adversarial disturbances, ensuring convergence within a fixed time.

Contribution

It presents a novel combination of game theory, barrier Lyapunov functions, and physics-informed learning to solve the complex HJI equation for robust control.

Findings

The method guarantees stabilization within a predefined time despite adversarial disturbances.

Simulation results confirm the effectiveness and robustness of the proposed approach.

The physics-informed learning algorithm successfully approximates the Nash equilibrium control strategy.

Abstract

We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system trajectories remain within a specified admissible set and converge to equilibrium in a predefined time despite adversarial disturbances. The control problem is formulated as a two-player zero-sum differential game, where the controller is a minimizing player and the adversary a maximizing player. We derive sufficient conditions for the existence of a saddle-point solution and safe predefined-time stability using a barrier Lyapunov function that satisfies a differential inequality and the steady-state Hamilton-Jacobi-Isaacs (HJI) equation. To address the analytical intractability of solving the HJI equation, we introduce a physics-informed learning algorithm that robustly learns the Nash safely predefined-time stabilizing control strategy. Simulation results demonstrate the efficacy and resilience of the proposed method in ensuring robust optimal safe predefined-time stabilization under adversarial disturbances.