Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach

Area of Science:

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

Background:

• Designing robust controllers for nonlinear systems with uncertainties is challenging.
• Takagi-Sugeno fuzzy models are widely used for nonlinear system representation.
• Parameter uncertainties and external disturbances degrade system performance and stability.

Purpose of the Study:

• To design robust adaptive stabilizing controllers for Takagi-Sugeno fuzzy systems.
• To address both norm-bounded parameter uncertainties and external disturbances.
• To ensure exponential convergence of system states to a controllable ball.

Main Methods:

• Utilized linear matrix inequality (LMI) techniques for controller synthesis.
• Developed two adaptive control strategies.
• Assumed norm-bounded parameter uncertainties with potential structure properties.
• Considered matching external disturbances that are norm-bounded but with unknown bounds.

Main Results:

• Guaranteed global, uniform, and exponential convergence of closed-loop system states.
• Achieved convergence to a ball in the state space with any pre-specified rate.
• Demonstrated that the ball's radius can be made arbitrarily small by tuning controller parameters.
• Validated the approach using a continuous stirred tank reactor (CSTR) control problem.

Conclusions:

• The proposed adaptive controllers effectively stabilize nonlinear Takagi-Sugeno fuzzy systems under uncertainties and disturbances.
• The LMI-based approach provides a systematic way to design controllers with desired performance specifications.
• The controller's ability to minimize the convergence ball radius offers enhanced control precision.