Dynamic boundary layer super‐twisting sliding mode control algorithm based on RBF neural networks for a class of leader‐follower multi‐agent systems

• Published in: International journal of robust and nonlinear control Vol. 34; no. 3; pp. 2109 - 2140
• Main Authors: Jia, Chao, Shangguan, Xuanyue, Zheng, Linxin
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.02.2024
• Subjects: Algorithms; Boundary layers; Control algorithms; Control methods; Control systems design; Control theory; Controllers; Convergence; dynamic boundary layer; Fault tolerance; leader‐follower multi‐agent system; Mathematical models; Neural networks; Radial basis function; RBF neural network; Robustness (mathematics); Sliding mode control; Stability analysis; super‐twisting sliding mode control; Twisting; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7073

In this paper, the consensus problem of robust sliding mode fault tolerance for a class of leader‐follower multi‐agent systems is discussed. Aiming at a second‐order multi‐agent system with unknown model uncertainty and external disturbance, a new super‐twisting sliding mode control method based on a dynamic boundary layer and neural network is proposed. Firstly, the super‐twisting controller is designed by introducing two new variables, the convergence speed of the control system is greatly improved, and the symbolic function is replaced by an improved dynamic boundary layer, which will be continuously adjusted with the system states, the tracking accuracy of the system is improved, and the chattering problem caused by symbolic function is overcome effectively. Secondly, an radial basis function neural network is used to realize the adaptive approximation to the completely unknown model, so that the controller does not need to depend on the precise mathematical model of the controlled system, and the stability of the closed‐loop system is ensured by adjusting the adaptiveweight. Thirdly, the stability of the whole system is analyzed by the Lyapunov method, and the upper bound of robust consensus error is given by constructing an equivalence relation, meanwhile, the upper bound of the final convergence of the sliding variable in the dynamic boundary layer is analyzed. Finally, the simulation results for a second‐order system show the superior performance of the proposed control algorithm, then it is extended to a class of application systems, and the same conclusion is obtained.