Low-cost adaptive prescribed time tracking control for switched nonlinear systems

ABSTRACT

This paper addresses a low-cost adaptive prescribed time tracking control strategy for switched nonlinear systems with input quantisation and unknown backlash-like hysteresis. Initially, a transformation function is introduced into the control design, which allows the tracking error of the controlled systems to a specified accuracy within a preassigned settling time. Unlike the existing prescribed time control scheme that only uses transformation function technique in the first step of the backstepping design, the transformation function is introduced to each step of the controlled systems, which makes only one adaptive parameter that needs to be updated online. Then, to synthesise a low-cost control scheme, a first-order sliding mode differentiator and a single-parameter estimation method are implemented based on the newly constructed coordinate transformations. Meanwhile, the Nussbaum technique successfully solves the effects caused by the unknown control direction, unknown backlash-like hysteresis and quantised input. All signals of the closed-loop systems are bounded under the proposed control scheme with arbitrary switching signal. Finally, the validity of the presented method is confirmed via two simulation examples.

KEYWORDS:

• Input quantisation
• low-cost adaptive control
• switched nonlinear systems
• unknown backlash-like hysteresis
• unknown control direction

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [62003052].

Notes on contributors

Jie Zhang

Jie Zhang received the B.S. degree in electrical engineering and automation from Yuncheng University, Yuncheng, China, in 2021. He is currently pursuing the M.S. degree in detection technology and automation device from Bohai University, Jinzhou, China.

Yingnan Pan

Yingnan Pan received the B.S. degree in mathematics and applied mathematics and the M.S. degree in applied mathematics from Bohai University, Jinzhou, China, in 2012 and 2015, respectively, and the Ph.D. degree in navigation guidance and control from Northeastern University, Shenyang, China, in 2019. He is currently an associate professor with Bohai University, Jinzhou, China. His current research interests include fuzzy control, adaptive control, event-triggered control and their applications.

Qing Lu

Qing Lu received the B.S. degree in automation from Hebei University of Technology, Tianjin, China, in 2013, the M.S. degree in control theory and control engineering from Bohai University, Jinzhou, China, in 2016 and the Ph.D. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2021. From 2017 to 2019, she was a Visiting Student with the School of Electrical and Electronic Engineering, University of Adelaide, Australia. She is currently a Lecturer at College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, China. Her current research interests include networked control systems, fuzzy control, model predictive control, event-triggered control and their applications.