Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Pure-feedback stochastic nonlinear systems present challenges due to input saturation.
• Nondifferential saturation nonlinearity complicates controller design.

Purpose of the Study:

• To develop an adaptive fuzzy tracking controller for pure-feedback stochastic nonlinear systems with input saturation.
• To ensure stability and performance of the closed-loop system.

Main Methods:

• Approximation of saturation nonlinearity using a smooth nonlinear function.
• Backstepping technique combined with the mean-value theorem.
• Design of an adaptive fuzzy tracking controller.

Main Results:

• All signals in the closed-loop system are bounded in probability.
• The system output converges to a small neighborhood of the desired reference signal (in the mean quartic value sense).
• Simulation results confirm the controller's effectiveness.

Conclusions:

• The proposed adaptive fuzzy controller effectively handles input saturation in stochastic nonlinear systems.
• The control scheme guarantees system boundedness and output convergence.
• This approach offers a robust solution for complex control problems.