Observer-Based Human-in-the-Loop Optimal Output Cluster Synchronization Control for Multiagent Systems: A Model-Free Reinforcement Learning Method

This article investigates the observer-based human-in-the-loop (HiTL) optimal output cluster synchronization control problem for nonlinear multiagent systems (MASs). First, the leader is designed to be nonautonomous, with the unknown time-varying input monitored by the human operator directly. To address the problem that leader’s output is not available to each follower, an observer is designed. This observer features practical prescribed-time convergence, and independence of prior knowledge of leader’s input. Then, an augmented system consisting of observer dynamics and follower dynamics is constructed and a cost function is formulated. Accordingly, the HiTL optimal output cluster synchronization control problem is transformed into a solution to the Hamilton-Jacobian–Bellman equation (HJBE). Subsequently, the off-policy reinforcement learning algorithm is utilized to learn the solution to HJBE without complete knowledge of the system dynamics. To alleviate computational burden, the single critic neural network (NN) is employed for the algorithm implementation, with the least square method applied for training the NN weights. Finally, the simulation results are presented to verify the validity of the designed control scheme.