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Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements
IEEE Transactions on Cybernetics
|September 9, 2021
Summary
This study introduces a fuzzy boundary control (FBC) for nonlinear delayed distributed parameter systems (DDPSs) using Takagi-Sugeno models. The method ensures exponential stability for DDPSs with boundary measurements, validated by simulations.
Area of Science:
- Control Theory
- Nonlinear Systems
- Partial Differential Equations
Background:
- Nonlinear delayed distributed parameter systems (DDPSs) present significant control challenges.
- Boundary control strategies are crucial for managing spatially distributed systems.
Purpose of the Study:
- To develop a fuzzy boundary control (FBC) strategy for nonlinear DDPSs using only boundary measurements (BMs).
- To ensure exponential stability of the closed-loop system despite time-varying delays.
Main Methods:
- Modeling nonlinear DDPSs using Takagi-Sugeno (T-S) fuzzy partial differential-difference equations (PDDEs).
- Designing the FBC using spatial linear matrix inequalities (SLMIs), Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method.
- Formulating SLMIs as linear matrix inequalities (LMIs) for controller design.
Main Results:
- The proposed FBC strategy guarantees exponential stability for nonlinear DDPSs under BMs.
- The control design effectively handles both fast-varying and slow-varying delays.
- Simulation examples demonstrate the practical effectiveness of the FBC approach.
Conclusions:
- The developed T-S fuzzy boundary control is a viable method for stabilizing nonlinear DDPSs.
- The use of SLMIs provides a systematic approach to designing controllers for such complex systems.
- This research contributes to advancing control strategies for systems with both spatial distribution and time delays.
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