Command filter‐based adaptive neural network controller design for uncertain nonsmooth nonlinear systems with output constraint

• Published in: International journal of adaptive control and signal processing Vol. 37; no. 2; pp. 474 - 496
• Main Authors: Xu, Qian, Zong, Guangdeng, Chen, Yunjun, Niu, Ben, Shi, Kaibo
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01-02-2023
• Subjects: Adaptive control; adaptive neural network; compensation signal; Control systems design; Controllers; Error compensation; Liapunov functions; Neural networks; Nonlinear systems; nonsmooth nonlinear systems; output constraint; Robot arms; the Levant's differentiator; Tracking control; Tracking errors
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3532

Summary
This paper investigates the command filter‐based adaptive neural network tracking control problem for uncertain nonsmooth nonlinear systems. First, an integral barrier Lyapunov function is introduced to deal with the symmetric output constraint and make the output comply with prescribed restrictions. Second, by the Filippov's differential inclusion theory and approximation theorem, the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system. Third, the Levant's differentiator is used to deal with the “explosion of complexity” problem. An error compensation mechanism is established to attenuate the effect of the filtering error on control performance. Then, an adaptive neural network controller is set up by resorting to the backstepping technique. It is strictly mathematically proved that the tracking error can converge to an arbitrarily small neighborhood of the origin and all the signals in the closed‐loop system are semi‐globally uniformly ultimately bounded. Finally, a numerical example and an application example of the robotic manipulator system are provided to demonstrate the availability of the proposed control strategy.