Fuzzy Control Under Spatially Local Averaged Measurements for Nonlinear Distributed Parameter Systems With...

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Nonlinear Dynamics

Background:

• Nonlinear-delayed distributed parameter systems (DDPSs) are challenging to control due to their complexity.
• Existing methods often struggle with fast-varying time delays and spatially distributed dynamics.

Purpose of the Study:

• To develop a robust fuzzy control (FC) strategy for nonlinear-delayed distributed parameter systems (DDPSs).
• To address systems described by parabolic partial differential-difference equations (PDdEs) with both fast and slow time delays.
• To ensure exponential stability of the closed-loop system using spatially local averaged measurements (SLAMs).

Main Methods:

• Derivation of a Takagi-Sugeno (T-S) fuzzy PDdE model to represent the nonlinear DDPSs.
• Design of an FC law using a Lyapunov-Krasovskii functional and SLAMs.
• Utilization of spatial linear matrix inequalities (SLMIs) for stability analysis and controller synthesis.
• Membership functions of the FC law are determined by measurement output, independent of the plant model.

Main Results:

• The proposed FC design guarantees exponential stability for the closed-loop DDPSs.
• The method effectively handles nonlinearities and time-varying delays inherent in the system.
• A numerical example validates the efficacy of the developed approach.

Conclusions:

• The fuzzy control under SLAMs provides a stable and effective control solution for nonlinear-delayed distributed parameter systems.
• This approach offers a promising direction for controlling complex systems with spatial dynamics and time delays.
• The independence of membership functions from the plant model simplifies practical implementation.