Robust Fuzzy Adaptive Tracking Control for Nonaffine Stochastic Nonlinear Switching Systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Stochastic Systems

Background:

• Nonaffine stochastic nonlinear switched systems present significant control challenges due to their complex dynamics and arbitrary switching.
• Existing control methods often struggle with nonlower triangular structures and completely nonaffine forms.

Purpose of the Study:

• To develop a robust trajectory tracking controller for nonaffine stochastic nonlinear switched systems.
• To address systems with nonlower triangular structures and unknown nonlinearities.

Main Methods:

• Fuzzy systems are utilized to approximate unknown nonlinearities.
• Backstepping and robust adaptive control techniques are combined with a common Lyapunov function approach.
• Lyapunov stability theory is employed to ensure system stability.

Main Results:

• The proposed controller guarantees semiglobal uniform ultimate boundedness in the fourth moment for all closed-loop signals.
• System output converges to a small neighborhood of the desired trajectory.
• The method effectively handles completely nonaffine forms and nonlower triangular structures.

Conclusions:

• The developed fuzzy adaptive control strategy provides a robust solution for trajectory tracking in challenging nonlinear switched systems.
• This approach overcomes limitations of previous methods by accommodating nonaffine and nonlower triangular system characteristics.
• The effectiveness of the control method is validated through simulation results.