Adaptive Optimal Output-Feedback Consensus Tracking Control of Nonlinear Multiagent Systems Using Two-Player Stackelberg Game

This article investigates the adaptive optimal output-feedback consensus tracking problem for nonlinear multiagent systems (MASs). Although adaptive optimal output-feedback control schemes for nonlinear systems have been developed recently, most results do not consider the two-way interaction between the state observer and its associated subsystem. To address this issue, we formulate the state-observer and the subsystem as a two-player Stackelberg game framework, where the state-observer acts as the follower-player and the subsystem acts as the leader-player. Such a framework helps us to reveal the two-way interaction between the subobserver and the subsystem. Based on this, we design the optimal auxiliary input of the state-observer and the optimal subsystem controller. We implement the optimal policy pair using integral reinforcement learning (IRL) and adaptive critic learning, which provides a critic-only structure. We prove that the Stackelberg-Nash equilibrium is reached and that the closed-loop signals are ultimately uniformly bounded (UUB). We demonstrate the effectiveness of the proposed scheme using a numerical simulation example.