Distributed Adaptive Dynamic Programming for Consensus Control of Multiagent Systems Within Hierarchical Stackelberg–Nash Game Framework

This article investigates the leader-follower consensus for nonlinear multiagent systems (MASs) and proposes an adaptive dynamic programming (ADP)-based hierarchical Stackelberg-Nash optimal game control method. Initially, a coupled performance index function associated with consensus errors is constructed. As the positive-definite function with the quadratic form is allocated to the constructed consensus errors-based performance index function, the original system stabilization problem is converted into the issue of seeking an optimal control strategy profile for the leader and followers. Under the hierarchical Stackelberg-Nash differential game framework, the optimal control strategies are derived in sequence and further proved to compose the equilibrium points of Stackelberg-Nash differential games. Afterward, based on the ADP technique, a modified single-critic neural network (NN) is implemented and the coupled Hamilton-Jacobi–Bellman (HJB) equation is approximately identified. Under the proposed control scheme, the leader-follower consensus of the considered MAS can be achieved while consuming less control cost. Meanwhile, all signals of the MAS are ensured to be uniformly ultimately bounded. Finally, a numerical simulation and an application to the electrode regulating system of the three-phase electric arc furnace are given to verify the effectiveness of the proposed control method.