Time-Varying Optimal Sliding-Mode Lag Formation Control for High-Order Nonlinear Multiagent Systems Based on Reinforcement Learning

This paper considers a type of high-order nonlinear multiagent systems (MASs), and the time-varying optimal lag formation control problem for such MAS is addressed. To eliminate the influences of the unknown system dynamics and external disturbance on single agent, a neural network (NN) identifier and disturbance observer based compensation controller is developed. Then, an optimal control law to ensure the practical time-varying lag formation for the MAS is introduced by exploiting the sliding-mode control (SMC) method and reinforcement learning (RL) technique. Finally, a numerical example is given to validate the effectiveness of the proposed optimal control law. Note to Practitioners—Recently, leader-following approach has been widely utilized to investigate the time-varying formation (TVF) control problem for various MASs. In fact, time delay is unavoidable during the process of the follower tracking the leader, it is more meaningful and reasonable to address the time-varying lag formation control problem of MASs. Moreover, most of the existing TVF control results ignore the optimal performance. Considering that a balance between system performance and control resources, it is also very significant and challenging to further tackle the optimal TVF control problem of MASs. In this paper, an RL-based time-varying optimal sliding-mode lag formation control strategy for high-order nonlinear MASs is developed, and an MAS consisting of four unmanned surface vehicles (USVs) is utilized to validate the effectiveness of the presented control strategy.