Prespecifiable fixed‐time control for a class of uncertain nonlinear systems in strict‐feedback form

• Published in: International journal of robust and nonlinear control Vol. 30; no. 3; pp. 1203 - 1222
• Main Authors: Cao, Ye, Wen, Changyun, Tan, Shilei, Song, Yongduan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.02.2020
• Subjects: adaptive control; backstepping; Convergence; Liapunov functions; Nonlinear systems; prespecifiable fixed‐time; Settling; State feedback; Tracking errors; uncertain nonlinear systems
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4820

Summary In this paper, we investigate the prespecifiable fixed‐time control problem for a class of uncertain nonlinear systems in strict‐feedback form, where the settling (convergence) time is not only bounded but also user‐assignable in advance. One of the salient features of the proposed method lies in the fact that it makes it possible to achieve any practically allowable settling time by using a simple and effective control parameter selection recipe. Both fixed‐time stabilization and fixed‐time tracking are considered for uncertain strict‐feedback systems. Firstly, by adding exponential state feedback and using fractional power integration as Lyapunov function candidate, a global stabilizing control strategy is developed. It is proved that all the system states converge to zero within prespecified fixed‐time with continuous and bounded control action. Secondly, under more general uncertain nonlinearities and external disturbances, an adaptive fixed‐time controller is derived such that the tracking error converges to a small neighborhood of zero within preassigned time. Theoretical results are also illustrated and supported by simulation studies.