Zero-Sum Differential Game Based Fault-Tolerant Control for a Class of Nonlinear Multi-Agent Systems With Communication Faults

This paper presents a distributed fault-tolerant control design for nonlinear second-order multi-agent systems (MAS) affected by communication faults caused by malicious cyber-attacks or intentional interference. The approach is implemented in two steps. First, a zero-sum differential game framework is established, where virtual controllers and fault-induced biases are treated as opposing players, minimizing and maximizing cost functions related to local tracking performance and fault tolerance. Second, optimal control policies are derived from the virtual control policies and the Hamiltonian-Jacobi-Bellman (HJB) equations. The adaptive dynamic programming (ADP) method is employed to estimate weights in the critic neural network (NN) in both steps. The proposed scheme ensures tracking performance and optimal control efficacy. Its effectiveness is validated through simulation studies with multiple spacecraft systems.