Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics

Background:

• Hysteretic systems present significant challenges in control due to their inherent memory effects and non-smooth dynamics.
• Achieving global output tracking in uncertain nonlinear systems with nonaffine structures is a complex problem in control theory.

Purpose of the Study:

• To develop a robust adaptive control algorithm for uncertain nonlinear hysteretic systems with nonaffine structures.
• To achieve global output tracking without requiring an explicit inverse model of the hysteresis.
• To enhance the control scheme's robustness against bounded disturbances.

Main Methods:

• A novel backstepping approach combined with hysteresis model properties.
• Development of a robust adaptive control algorithm.
• Adaptive estimation of bounded disturbance bounds.
• Rigorous mathematical proof of closed-loop system stability.

Main Results:

• A robust adaptive control algorithm is successfully developed for the specified class of systems.
• The algorithm guarantees global output tracking and closed-loop stability.
• The control scheme effectively handles bounded disturbances through adaptive estimation.
• No hysteresis inverse was required, simplifying the control design.

Conclusions:

• The proposed robust adaptive control scheme ensures global stability and output tracking for uncertain nonlinear hysteretic systems.
• The method's effectiveness is demonstrated through numerical examples, offering a practical solution for complex systems.
• This research contributes a novel control strategy applicable to systems exhibiting hysteresis and uncertainties.