Asynchronous Observer-Based Fault-Tolerant Optimal Control of Multiagent Systems

In this article, the optimal consensus problem for a class of nonlinear multiagent systems in discrete-time case is investigated under jump faults and false data injection (FDI) attacks. First, a general fault model with coefficients obeying a semi-Markov process is introduced into system dynamics. A joint state and fault observer based on the hidden semi-Markov model is designed to estimate both the agent's state and the fault signals. Sufficient conditions for the existence of observer gains are established by constructing the stochastic Lyapunov function with hidden mode, observed mode, and elapsed time dependencies. Based on the observed states, we reconstruct the local performance metric functions of agents and design a policy-value iteration algorithm to address the multiplayer game problem. Then, an neural network policy-value iteration approximation algorithm is proposed, which obtains an approximate Nash equilibrium solution of the multiplayer games. Further, a secure fault-tolerant optimal consensus controller with fault compensation and attack attenuation terms is designed to achieve optimal tracking control, and the stability of the neighbor tracking error system is rigorously demonstrated. Finally, illustrative example and comparison simulations are provided to verify the validity and applicability of the proposed results.