Zero-Error Prescribed-Time Tracking Control for Switched Non-Square MIMO Nonlinear Systems Subject to Asymmetric Time-Varying Output Constraints

Ying Liu, Hui Wang (), Quanxin Zhu () and Fujin Jia
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Ying Liu: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Hui Wang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Quanxin Zhu: CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Fujin Jia: School of Electrical Engineering and Automation, Anhui University, Hefei 230039, China

Mathematics, 2025, vol. 13, issue 6, 1-22

Abstract: Previous studies typically assume that output constraints are symmetric or time-invariant. However, effectively addressing asymmetric and time-varying output constraints remains an unsolved issue, especially in the case of switched non-square multi-input multi-output (MIMO) nonlinear systems. To tackle this challenge, this paper first establishes a prescribed-time (PT) Lyapunov criterion for switched nonlinear systems. Second, an asymmetric nonlinear mapping (ANM) method is proposed to handle asymmetric time-varying output constraints. Compared to the barrier Lyapunov function (BLF) approach, the ANM method relaxes the initial output conditions and the constraint functions are not necessarily required to be opposite in sign. Finally, a PT tracking controller is designed for a class of switched MIMO nonlinear systems with a non-square control coefficient matrix by using the time-varying gain technique. This controller achieves zero-error tracking within the prescribed time while ensuring that output constraints are satisfied. The effectiveness of the proposed control strategy is validated through numerical and simulation examples.

Keywords: switched MIMO nonlinear systems; prescribed-time tracking control; time-varying output constraints; non-square control coefficient matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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