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

Nick-Marios T. Kokolakis; Shanqing Liu; Jerome Darbon; Rahul Mangharam; George Em Karniadakis

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arXiv · 2511.15018

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

Nick-Marios T. Kokolakis·Shanqing Liu·Jerome Darbon·Rahul Mangharam·George Em Karniadakis

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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.

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Nick-Marios T. Kokolakis, Shanqing Liu, Jerome Darbon, Rahul Mangharam, George Em Karniadakis. 2025-11-19. Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach. https://arxiv.org/abs/2511.15018

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