Optimized backstepping‐based finite‐time containment control for nonlinear multi‐agent systems with prescribed performance

• Published in: Optimal control applications & methods Vol. 45; no. 5; pp. 2364 - 2382
• Main Authors: Tang, Li, Zhang, Liang, Xu, Ning
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.09.2024
• Subjects: Algorithms; Containment; containment control; Control methods; Control systems; identifier‐critic‐actor architecture; Machine learning; multi‐agent systems; Neural networks; Nonlinear control; Nonlinear systems; Optimization; optimized backstepping; Performance evaluation; prescribed performance; Time optimal control; Tracking errors; Transient performance
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.3160

In this article, a finite‐time optimal containment control method is proposed for nonlinear multi‐agent systems with prescribed performance. First, a neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. The algorithm employs an identifier‐critic‐actor architecture, where the identifiers, critics and actors are used to estimate the unknown dynamics, evaluate the system performance, and optimize the system, respectively. Subsequently, in order to guarantee the transient performance of the tracking error, the original system is converted into an equivalent unconstrained system. Then, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. Furthermore, by using the Lyapunov stability theorem, it is verified that all signals are semi‐globally practical finite‐time stable, and all followers can converge to a convex region formed by multiple leaders. Finally, the effectiveness of the proposed scheme is demonstrated by a practical example. This paper proposes a finite‐time optimal containment control method for nonlinear multi‐agent systems with prescribed performance. A neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. Moreover, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. The effectiveness of the proposed scheme is demonstrated by a practical example.