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Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems
Hiroshi Ohtake1, Kazuo Tanaka, Hua O Wang
1Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan. hohtake@mce.uec.ac.jp
Summary
This study introduces an effective switching fuzzy controller for nonlinear systems. The novel approach simplifies controller design using an augmented system and linear matrix inequalities (LMIs).
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear System Dynamics
Background:
- Previous work established switching fuzzy models and Lyapunov functions for open-loop nonlinear systems.
- Controller design conditions based on switching Lyapunov functions were previously defined using bilinear matrix inequalities, posing numerical challenges.
Purpose of the Study:
- To design a switching fuzzy controller for nonlinear systems.
- To overcome the numerical difficulties associated with bilinear matrix inequalities in controller design.
- To develop an effective and practical LMI-based approach for switching fuzzy controller design.
Main Methods:
- A switching fuzzy model represents the nonlinear system dynamics.
- An augmented system, combining the switching fuzzy model with a stable linear system, is introduced.
- Controller design conditions are reformulated using linear matrix inequalities (LMIs) via the augmented system.
Main Results:
- The proposed augmented system approach transforms controller design conditions into LMIs.
- This LMI-based formulation enables effective numerical design of the switching fuzzy controller.
- A design example demonstrates the practical utility and effectiveness of the developed approach.
Conclusions:
- The LMI-based approach provides an efficient method for designing switching fuzzy controllers for nonlinear systems.
- This methodology simplifies the numerical implementation compared to previous bilinear matrix inequality-based techniques.
- The approach is applicable to piecewise linear control research areas.
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