Distributed Optimal Consensus Control for Multiagent Systems With Input Delay

This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

I. Introduction

With the rapid development of computation and communication, coordination control of networked multiagent systems (MASs) has received considerable attention due to their broad applications in various fields, such as unmanned aerial vehicles [1], automated highway systems [2], satellite clusters [3], multiple rigid systems [4], mobile robots [5], and so on. As one of the fundamental issues of coordination control, consensus control [6]–[11] aims at designing a control protocol based on local information that enables all the agents to reach an agreement regarding certain quantity of interest. We refer to the surveys [12]–[14] on the recent developments of consensus control for MASs.