Functional Observer Design for T-S Fuzzy Systems With Complex Unmeasurable Premise Variables

Area of Science:

• Control Engineering
• Fuzzy Systems Theory
• Nonlinear Control

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling complex nonlinear systems.
• Designing functional observer-controllers (FOC) is challenging when premise variables are unmeasurable and nonlinear.
• Unmeasurable premise variables (UPV) introduce significant difficulties in observer and controller design.

Purpose of the Study:

• To develop a novel method for functional observer-controller (FOC) design in T-S fuzzy systems.
• To address the challenge of complex, unmeasurable premise variables (UPV) with nonlinear characteristics.
• To ensure robust stability and accurate estimation for systems with UPVs.

Main Methods:

• A new transformation technique is proposed to linearize the nonlinear unmeasurable premise variable (UPV).
• The functional observer-controller (FOC) is designed to estimate the linearized premise variable.
• Observer and controller gains are derived using convex robust and stability conditions.
• A robust separation principle is applied to stabilize the estimation and control error system.

Main Results:

• The proposed transformation effectively linearizes the complex UPV.
• The designed FOC successfully estimates the premise variable.
• Robust stability conditions ensure the stability of the estimation and control error system.
• Simulation examples validate the effectiveness of the developed FOC design method.

Conclusions:

• The presented method provides an effective solution for FOC design in T-S fuzzy systems with nonlinear UPVs.
• The approach ensures robust stability and accurate estimation, overcoming challenges posed by unmeasurable variables.
• This work contributes to the advancement of control strategies for complex nonlinear systems.