Fault-Tolerant Optimal Consensus for Multiagent Systems: A Fuzzy-Based Game Approach

This article investigates the fault-tolerant optimal consensus problem of nonlinear discrete-time leader-following multiagent systems via nonzero-sum graphical games. First, a stochastic actuator fault model considering actuator effectiveness loss is established on account of semi-Markov processes under discrete-time settings, which can cover the existing multiplicative actuator fault models and is more general. Considering the multimodality of stochastic actuator faults, the cost function of each agent is reconstructed by combining semi-Markov kernel and weighted sum approach. By the optimality principle as well as the discrete-time Bellman equation, the hybrid policy-value iteration algorithm is developed to seek the Nash equilibrium of multiagent nonzero-sum games, which integrates the advantages of policy iteration and value iteration algorithms and can improve the convergence performance of both. Then, we propose the fault-tolerant optimal controller based on the projection estimation approach. The convergence of the iterative algorithm, as well as the uniformly ultimately boundedness for the tracking error and the estimation error of fault parameters are proved, respectively. Moreover, the generalized fuzzy hyperbolic model is adopted to implement approximately the proposed hybrid policy-value iteration algorithm, which can reduce the number of updated weights and the computational burden. Finally, two simulation examples are provided to justify the effectiveness of the presented approach.