Robust Adaptive Fuzzy Control of a Class of Uncertain Nonlinear Systems With Unstable Dynamics and Mismatched...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Fuzzy Logic Systems

Background:

• Uncertain nonlinear systems often exhibit unstable zero dynamics, posing significant control challenges.
• Existing methods may not adequately address nonlinear uncertainties and mismatched external disturbances in these systems.
• Input-to-state practical stability of zero dynamics is a common but restrictive assumption.

Purpose of the Study:

• To develop a robust adaptive fuzzy control strategy for uncertain nonlinear systems with unstable zero dynamics.
• To ensure asymptotic stability of the zero dynamics and achieve accurate tracking control.
• To handle nonlinear uncertainties and mismatched external disturbances without assuming input-to-state practical stability.

Main Methods:

• A robust adaptive fuzzy control method is developed by integrating fuzzy logic with the backstepping technique.
• An ideal virtual control function is designed to achieve asymptotic stability of the zero dynamics.
• An actual controller is constructed using non-negative functions and backstepping, incorporating an auxiliary signal to manage unavailable virtual reference signals.

Main Results:

• The proposed controller guarantees asymptotic stability for the zero dynamics with suboptimal performance.
• The tracking error for the ideal virtual control signal converges to a priori accuracy, irrespective of external disturbances.
• The method is validated through direct application to a partially linear zero dynamics case and demonstrated on a two-inverted pendulum system.

Conclusions:

• The developed robust adaptive fuzzy control method effectively stabilizes uncertain nonlinear systems with unstable zero dynamics.
• The approach successfully addresses nonlinear uncertainties and mismatched disturbances, offering improved control performance.
• The technique provides a valuable tool for robust control design in complex nonlinear systems.