ADP-Based Robust Resilient Control of Partially Unknown Nonlinear Systems via Cooperative Interaction Design

Abstract

This article studies resilient control problems for partially unknown nonlinear systems subjected to malicious injections on the control input signals. The injection model is assumed to be Lipschitz continuous and derivable regarding an unknown bounded signal, and the signal is produced from an unknown finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> -gain dynamical system. First, based on neural network identifier and adaptive dynamic programming techniques, a novel controller with two fictitious dynamical systems, as co-workers of the closed-loop systems resisting attacks, is proposed. Furthermore, a cooperative interaction framework between the virtual dynamical systems and the closed-loop systems is developed, and through optimal control theory and Lyapunov function methods, it is proved that, the robust resilient controller designed in the framework ensures the attacked system states are uniformly ultimately bounded. Contrary to the presented approach, the impact of attacks is not considered in the existing results, then the stability for partially unknown nonlinear systems might not be guaranteed. Two illustrative examples validate the presented method.