Learning-based optimal cooperative control using edge-based triggering strategy

Existing studies on event-triggered output tracking control have focused only on addressing steady errors while neglecting transmit errors, which leads to the obtained results in a non-optimal implementation fashion. To solve this problem, this paper adopts a reinforcement learning algorithm to investigate the optimal output tracking control of heterogeneous multi-agent systems with a novel event-triggered mechanism. First, different from existing model-based predictor method for each agent, a novel edge-based predictor using the relative state information is proposed to estimate the relative state information among agents during the time interval between two adjacent triggering instants. Then, the predicted relative state is put forwarded to design event-triggered distributed observer to provide the state estimation of the leader's information, and a novel event-triggered condition based on the control input signal is developed. As a result, the proposed edge-based distributed observer method not only avoids continuous communication among followers, the leader and its children, and Zeno behavior, but also the explicit control input signal can be protected from the view of privacy protection. Second, the state feedback control policy under a reinforcement learning method is considered to achieve the model-based optimal output tracking control, where the optimal control policy is learned by solving the Bellman equation iteratively. Beside, the model-free optimal output tracking control is also achieved by verifying the rank condition based on the collected system data without relying on accurate system dynamics. It is shown that the proposed algorithm ensure the model-free optimal output tracking control without continuous communication and prior system knowledge. Finally, the effectiveness of the proposed theoretical algorithm is verified using a simulation example.