Decentralized Observer-Based Controller Synthesis for a Large-Scale Polynomial T-S Fuzzy System With Nonlinear...

Area of Science:

• Control Systems Engineering
• Nonlinear System Analysis
• Fuzzy Logic Systems

Background:

• Large-scale nonlinear systems present significant control challenges due to complex interconnections.
• Existing observer-based controllers often require strict bound constraints on nonlinear interconnection terms, limiting their applicability.
• Polynomial T-S fuzzy systems offer a framework to model nonlinear systems while potentially reducing modeling errors and fuzzy rule complexity.

Purpose of the Study:

• To propose a novel decentralized observer-based controller for large-scale nonlinear systems with arbitrary nonlinear interconnections.
• To develop a controller that does not require prior bounding of nonlinear interconnection terms, offering greater flexibility.
• To design an observer capable of simultaneously estimating unmeasurable states and unknown nonlinear interconnection terms.

Main Methods:

• Modeling the large-scale nonlinear system using polynomial Takagi-Sugeno (T-S) fuzzy systems.
• Developing a new observer form utilizing an unknown input method to estimate unmeasurable states and interconnection terms.
• Employing Lyapunov functions and the sum-of-squares (SOS) technique to derive observer and controller design conditions.

Main Results:

• A decentralized observer-based controller was successfully synthesized for large-scale nonlinear systems.
• The proposed method accommodates arbitrary nonlinear interconnection functions without requiring bound constraints.
• The observer effectively estimates unmeasurable states and unknown interconnection terms, which are then used for system stabilization.
• Two numerical examples validated the effectiveness and advantages of the proposed approach.

Conclusions:

• The developed observer-based controller provides a more relaxed and practical approach for controlling large-scale nonlinear systems.
• The novel observer design, capable of estimating unknown states and interconnections, represents a significant advancement.
• The method demonstrates potential for broader application in complex nonlinear system control where interconnection terms are difficult to bound.