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 cons...

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Vydáno v:	IEEE transactions on systems, man, and cybernetics. Systems Ročník 55; číslo 6; s. 4286 - 4300
Hlavní autoři:	Zhang, Haoyan, Zhang, Yingwei, Zhao, Xudong, Su, Chun-Yi
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	IEEE 01.06.2025
Témata:	Artificial neural networks Differential games Distributed adaptive dynamic programming (ADP) Dynamic programming Games hierarchical Stackelberg-Nash game leader-follower consensus Multi-agent systems Nash equilibrium nonlinear multiagent systems (MASs) Optimal control Performance analysis single-critic neural network (NN) Topology
ISSN:	2168-2216, 2168-2232
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Abstract	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.
AbstractList	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.
Author	Zhang, Yingwei Zhao, Xudong Su, Chun-Yi Zhang, Haoyan
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SubjectTerms	Artificial neural networks Differential games Distributed adaptive dynamic programming (ADP) Dynamic programming Games hierarchical Stackelberg-Nash game leader-follower consensus Multi-agent systems Nash equilibrium nonlinear multiagent systems (MASs) Optimal control Performance analysis single-critic neural network (NN) Topology
Title	Distributed Adaptive Dynamic Programming for Consensus Control of Multiagent Systems Within Hierarchical Stackelberg-Nash Game Framework
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