Distributed observer-based hierarchical optimal consensus tracking with dynamic event-triggered adaptive dynamic programming

Constraints on the communication topology bring challenges to optimal consensus protocol design. This paper investigates an observer-based optimal consensus tracking problem with a dynamic event-triggered mechanism for nonlinear multi-agent systems. Followers have access to only part of the states of the leader. The control process is completed hierarchically with two layers. In the distributed observer layer, an extended distributed observer is designed for each follower to reconstruct states of the leader by exchanging local estimated information with its neighbours. Parameters are selected step by step instead of solving linear matrix inequalities, guaranteeing the solvability of the observer. In the decentralized protocol layer, a dynamic event-triggered adaptive dynamic programming algorithm is designed for tracking the observer state, which serves as a reference. Inter-event time slots are enlarged by introducing a positive inner variable with first-order filter dynamics. Asymptotic stability of the tracking error and ultimately uniformly bounded property are proven rigorously. Finally, an illustrative example validates the effectiveness of the proposed design.