Adaptive Finite-Time Controller Design for T-S Fuzzy Systems.

Area of Science:

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

Background:

• Takagi-Sugeno (T-S) fuzzy dynamic models are widely used for nonlinear systems.
• Parametric uncertainties pose significant challenges in controlling these systems.
• Finite-time stabilization is crucial for applications requiring rapid response.

Purpose of the Study:

• To develop an adaptive finite-time stabilization control scheme for T-S fuzzy systems with parametric uncertainties.
• To address the challenge of controller singularity in adaptive finite-time control design.
• To provide constructive procedures for controller synthesis and estimate convergence time.

Main Methods:

• Utilizing finite-time Lyapunov theorem for stability analysis.
• Employing an adaptive backstepping-like method for controller design.
• Introducing augmented dynamics to facilitate the construction of finite-time Lyapunov functions.

Main Results:

• A novel adaptive state feedback control scheme is proposed for T-S fuzzy systems.
• Finite-time convergence of the closed-loop adaptive control system is demonstrated.
• The proposed method effectively avoids potential controller singularity issues.
• Constructive procedures for controller design and finite-time upper bound estimation are provided.

Conclusions:

• The developed adaptive control approach effectively achieves finite-time stabilization for uncertain T-S fuzzy systems.
• The method offers practical advantages by avoiding controller singularity.
• Numerical examples validate the effectiveness and practicality of the proposed control strategy.