Exact-Optimal Consensus of Uncertain Nonlinear Multi-Agent Systems Based on Fuzzy Approximation

This paper is concerned with the distributed optimal consensus problem of multi-agent systems with uncertain nonlinear dynamics. The essential work of this paper is the development of an exact-optimal consensus control methodology via fuzzy adaptive control technique. Specially, an optimal signal generator for each agent is established to cooperatively estimate the accurately global optimal solution. Subsequently, a novel fuzzy adaptive controller is designed with the aid of command filtered backstepping and adaptive compensation technique, making it powerful enough to the fuzzy approximate error and filtering error. Thereby, it provides a concise optimal consensus control algorithm for strict-feedback nonlinear systems, which avoids the requirement that the gradient of the local cost function is high-order differentiable. Based on Lyapunov stability theory, it is proven that the outputs of all agents synchronize to an optimal agreement with asymptotic convergence; i.e., the exact-optimal consensus is able to be guaranteed under the proposed control approach. Finally, simulation studies and comparisons are presented to show the effectiveness of the proposed control approach. Note to Practitioners—This paper addresses the distributed optimal consensus problem of nonlinear multi-agent systems with uncertain dynamics, which is more challengeable. It is the first effort to study the exact-optimal consensus control problem via function approximation technique. Through constructing multiple optimal signal generators to cooperatively estimate the accurately global optimal solution, the distributed optimal consensus control is converted into an asymptotic tracking control. Then, a concise optimal consensus control is proposed by command filtered backstepping technique, which is easy to implement in practice. The developed control protocol can be applied to unmaned swarm systems, and it has contributions to academic and practical applications.