Adaptive control of nonlinear pure-feedback systems with output constraints: Integral barrier Lyapunov functional approach

• Published in: International journal of control, automation, and systems Vol. 13; no. 1; pp. 249 - 256
• Main Authors: Kim, Bong Su, Yoo, Sung Jin
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.02.2015; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Adaptive control; Analysis; Approximation; Barriers; Closed loop systems; Control; Control theory; Controllers; Design; Design engineering; Dynamical systems; Engineering; Feedback; Feedback control systems; Integrals; Mechatronics; Neural networks; Nonlinear dynamics; Nonlinearity; Regular Paper; Robotics; Studies; Theorems; 제어계측공학; dynamic surface design; pure-feedback systems; Adaptive control; integral barrier Lyapunov functional
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-014-0018-3

This paper studies an adaptive control problem of completely non-affine pure-feedback systems with an output constraint. The implicit function theorem and the mean value theorem are employed to deal with unknown output-constrained non-affine nonlinearities. Then, a dynamic surface design approach based on an appropriate Integral Barrier Lyapunov Functional is presented to design an adaptive controller ensuring both the constraint satisfaction and the desired tracking ability. For the controller design, the function approximation technique using neural networks is used for estimating unknown nonlinear terms with control direction nonlinearities. It is shown that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin while the output constraint is never violated.