Adversarial Physics-Informed Learning for Robust Optimal Safe Control in Time-Critical Environments: A Game-Theoretic Approach

Nick-Marios Kokolakis, Jerome Darbon, Rahul Mangharam, George Em Karniadakis

Keywords: Safe and resilient autonomy, robust optimal feedback control, differential games, physics-informed neural networks, predefined-time stability

TL;DR: A physics-informed learning framework for robust optimal safe control of autonomous systems in adversarial and time-critical environments.

Abstract: Autonomous systems operating in adversarial and time-critical environments require strategic decision-making mechanisms that ensure safety, robustness, and performance. Safe predefined-time stability characterizes parameter-dependent nonlinear dynamical systems whose trajectories starting in a set of admissible states remain within the set and converge to an equilibrium point within a predefined time. In this paper, we develop a game-theoretic framework to address a robust optimal safe predefined-time stabilization problem for parameter-dependent nonlinear dynamical systems subject to an adversary with nonquadratic performance measures. In particular, the robust optimal safe predefined-time stabilization problem is formulated as a two-player zero-sum differential game, wherein the controller is a minimizing player and the adversary is a maximizing player. Sufficient conditions for the existence of a saddle-point solution to the zero-sum game and closed-loop system safe predefined-time stability are derived. Specifically, safe predefined-time stability of the closed-loop system is guaranteed via a barrier Lyapunov function satisfying a differential inequality while serving as a solution to the steady-state Hamilton–Jacobi–Isaacs (HJI) equation ensuring Nash equilibrium. Since the steady-state HJI equation is typically intractable to solve analytically, we construct an adversarially robust physics-informed machine learning algorithm to learn the safely predefined-time stabilizing solution to the steady-state HJI equation. Simulation results illustrate the efficacy of the proposed framework.

Submission Number: 2