Fixed-Time Fuzzy Control for a Class of Nonlinear Systems

• Published in: IEEE transactions on cybernetics Vol. 52; no. 5; pp. 3880 - 3887
• Main Authors: Sun, Yumei, Wang, Fang, Liu, Zhi, Zhang, Yun, Chen, C. L. Philip
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive fuzzy control; Adaptive systems; backstepping; Control systems; Design parameters; fixed-time control; Fuzzy control; Fuzzy logic; Fuzzy systems; Nonlinear systems; Nonlinearity; Stability analysis; Stability criteria; Tracking control; Upper bound; Upper bounds
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.3018695

Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.