Stable adaptive probabilistic Takagi-Sugeno-Kang fuzzy controller for dynamic systems with uncertainties

Area of Science:

• Control Engineering
• Fuzzy Logic Systems
• Nonlinear Control Theory

Background:

• Nonlinear systems present significant control challenges due to their complex dynamics and uncertainties.
• Existing fuzzy logic controllers, such as Mamdani-type systems, have limitations in system size and learning accuracy.
• Probabilistic methods offer potential for handling uncertainties in nonlinear control but require integration with robust control strategies.

Purpose of the Study:

• To develop a novel adaptive probabilistic Takagi-Sugeno-Kang fuzzy PID (APTSKF-PID) scheme for enhanced nonlinear system control.
• To leverage the strengths of TSK fuzzy logic and probabilistic methods for improved control performance and robustness.
• To validate the effectiveness of the proposed APTSKF-PID controller in engineering applications involving nonlinear dynamical plants.

Main Methods:

• Development of an adaptive probabilistic Takagi-Sugeno-Kang fuzzy PID (APTSKF-PID) controller.
• Integration of TSK fuzzy logic for superior system size and learning accuracy.
• Incorporation of probabilistic processing for handling system uncertainties.
• Utilization of Lyapunov functions for tuning controller parameters and ensuring stability.
• Tuning of probability parameters to enhance controller flexibility and performance.

Main Results:

• The APTSKF-PID scheme demonstrates superior performance in controlling nonlinear systems compared to existing methods.
• The controller effectively handles external disturbances, random noise, and a wide range of system uncertainties.
• Lyapunov function-based tuning ensures controlled system stability.
• Tuning probability parameters provides additional flexibility and improves overall control performance.

Conclusions:

• The developed APTSKF-PID scheme offers a highly effective and robust solution for controlling complex nonlinear systems.
• The controller's ability to manage uncertainties and disturbances makes it suitable for demanding engineering applications.
• The integration of TSK fuzzy logic and probabilistic methods represents a significant advancement in nonlinear control technology.