Event-triggered optimal containment control for multi-agent systems subject to state constraints via reinforcement learning

• Published in: Nonlinear dynamics Vol. 109; no. 3; pp. 1651 - 1670
• Main Authors: Xu, Jiahong, Wang, Lijie, Liu, Yang, Xue, Hong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2022; Springer Nature B.V
• Subjects: Algorithms; Automation; Automotive Engineering; Classical Mechanics; Containment; Control; Control algorithms; Control systems; Controllers; Design; Dynamical Systems; Engineering; Game theory; H-infinity control; Machine learning; Mechanical Engineering; Multiagent systems; Optimal control; Original Paper; Systems stability; Vibration; Zero sum games; Event-triggered control; Containment control; State constraints; Reinforcement learning
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-022-07513-4

The paper addresses an event-triggered H ∞ containment control problem for multi-agent systems (MASs) with state constraints. Initially, the problem of state constraints is formulated as an equivalent unconstrained case by designing proper barrier functions. After that, the H ∞ optimal control problem is transformed into a two-player zero-sum game, and the H ∞ containment performance can be realized by obtaining the Nash equilibrium for zero-sum game. Then a novel event-triggered condition is designed for the optimal control and the worst disturbance. Compared with the existing event-triggered control results, the restriction on the disturbance attenuation level is relaxed. In addition, to further solve the event-triggered Hamilton–Jacobi–Isaacs equation (HJIE), a simplified reinforcement learning algorithm based on actor-critic-disturbance network is proposed by calculating the negative gradient of a constructed simple positive function. Meanwhile, such an algorithm can remove the requirement of persistent excitation condition. We also prove that, with the proposed effective strategy, all followers are driven into the convex hall spanned by multiple leaders and the state of each follower does not violate the desired set. Finally, the effectiveness of the proposed scheme is verified by two simulation examples.