Optimal Robust State Feedback Control Using Physics-Informed Neural Networks

Abstract

This paper presents a unified framework for optimal and robust state feedback control based on Physics-Informed Neural Networks. Traditional approaches to nonlinear optimal control, such as Hamilton–Jacobi–Bellman methods and dissipativity-based robustness analysis, suffer from the curse of dimensionality and rely on intractable analytical expressions for value functions or storage functions. To overcome these limitations, we formulate the robust optimal control problem as a physics-informed learning task in which the system dynamics, a Hamilton–Jacobi–Isaacs equation, and robustness constraints inspired by nonlinear ℒ2-gain and passivity theory are embedded directly into the PINN loss structure. The resulting neural architecture simultaneously approximates the value function and its gradient, enabling the synthesis of a robust state feedback law without discretization or linearization. We provide conditions under which the proposed approach preserves key robustness properties of dissipative systems and demonstrate its effectiveness through numerical examples.