Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

Wen-Jer Chang,Ming-Hsuan Tsai,Chin-Lin Pen

doi:10.3390/app11062833

Wen-Jer Chang, Ming-Hsuan Tsai + Show 1 more

Open Access

https://doi.org/10.3390/app11062833

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Journal: Applied sciences	Publication Date: Mar 22, 2021
Citations: 15	License type: CC BY 4.0

Affiliation: National Taiwan Ocean University

Abstract

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

Highlights

Discrete-Time Singular Systems via Singular systems, called descriptor systems or implicit systems, are important in the control field since their general representation
Because of the algebraic equations for the singular models, there may exist more than one solution
It results in the unwanted impulse terms that emerged in state trajectories to destroy singular systems’ stability

Summary

Introduction

Discrete-Time Singular Systems via Singular systems, called descriptor systems or implicit systems, are important in the control field since their general representation. To discuss the stabilization issue of nonlinear systems, the T-S fuzzy modeling approach was first proposed in [13]. The state feedback controller was constructed to stabilize the T-S fuzzy singular systems. The observer-based PD fuzzy control scheme is still an open problem for the discrete-time nonlinear systems to the best of the authors’ knowledge. The motivation of this paper is to overcome the above difficulty and develop a reasonable observer-based PD feedback fuzzy control scheme for discrete-time nonlinear singular systems. For the advantages of T-S fuzzy models and the motivations mentioned above, the stabilization problem of observer-based control for discrete-time T-S fuzzy singular systems was studied in this paper. The observer-based fuzzy controller was designed to reasonably use the PD feedback scheme in discrete-time cases.

System Descriptions and Problem Statements

Main Results

A Numerical Example

Conclusions