Open Access

ARTICLE

Optimal Fuzzy Tracking Synthesis for Nonlinear Discrete-Time Descriptor Systems with T-S Fuzzy Modeling Approach

Yi-Chen Lee¹, Yann-Horng Lin², Wen-Jer Chang^2,*, Muhammad Shamrooz Aslam^3,*, Zi-Yao Lin²

1 Department of Information Management, National Dong Hwa University, Hualien, 974, Taiwan
2 Department of Marine Engineering, National Taiwan Ocean University, Keelung, 202, Taiwan
3 Artificial Intelligence Research Institute, China University of Mining and Technology, Xuzhou, 2211106, China

* Corresponding Authors: Wen-Jer Chang. Email: ; Muhammad Shamrooz Aslam. Email:

Computer Modeling in Engineering & Sciences 2025, 143(2), 1433-1461. https://doi.org/10.32604/cmes.2025.064717

Received 21 February 2025; Accepted 17 April 2025; Issue published 30 May 2025

Abstract

An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation (PDC) approach and the Proportional-Difference (P-D) feedback framework. Based on the Takagi-Sugeno Fuzzy Descriptor Model (T-SFDM), a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems, which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process. Leveraging the P-D feedback fuzzy controller, the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system. In view of the disturbance problems, a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy. To achieve a better balance between state and control responses, the H₂ performance requirement is considered and a minimization constraint is applied to optimize the H₂ index. It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems. Extending the Lyapunov theory, a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints. Finally, two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.

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Keywords

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