Optimal Control on Finite-Time Consensus of the Leader-Following Stochastic Multiagent System With Heuristic Method

Abstract

In this paper, the optimization of the finite-time consensus of a multiagent system is studied when the leader is disturbed by white noise. Different from the consensus problem itself, this paper is devoted to optimizing the performance of the consensus and the constructive method and martingale method are used to guarantee the effectiveness of the optimization. Another contribution is that the problem of the optimal control with the piecewise constant controller gains under a stochastic environment is solved, and the reformed dynamic principle and the reformed Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs) are proposed by using the splitting method and Feynman–Kac formula. Furthermore, since the multiagent system often runs on a high-dimensional space, a heuristic method is proposed based on the derivation of the reformed HJB PDEs and the scalar of the computational complexity of the PDEs is equivalent to that of a system of ordinary differential equations with the same dimensions when the multiagent system can be described as a piecewise linear system. Finally, the heuristic method is compared with usual filtering methods for solving engineering problems by a numerical example and it is found that the heuristic method achieves higher precision in finite time.