Fuzzy Adaptive Quantized Control for a Class of Stochastic Nonlinear Uncertain Systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Fuzzy Logic Systems

Background:

• Existing research primarily addresses quantized stabilization, leaving quantized tracking problems less explored.
• Stochastic strict-feedback nonlinear systems present challenges due to uncertain nonlinearities and unknown stochastic disturbances.
• Quantized input signals introduce significant technical difficulties in control system design.

Purpose of the Study:

• To develop a fuzzy adaptive control approach for stochastic strict-feedback nonlinear systems with quantized input signals.
• To address the quantized tracking problem, extending beyond stabilization.
• To overcome the challenges posed by piecewise quantized inputs in control systems.

Main Methods:

• A novel nonlinear decomposition of the quantized input signal is proposed.
• Fuzzy logic systems' universal approximation capability is utilized.
• A fuzzy adaptive tracking controller is constructed using the backstepping technique.

Main Results:

• The proposed controller ensures that the tracking error converges to a neighborhood of the origin in probability.
• All signals within the closed-loop system are demonstrated to remain bounded in probability.
• The effectiveness of the fuzzy adaptive control approach is validated through a practical example.

Conclusions:

• The developed fuzzy adaptive approach effectively handles quantized tracking problems in stochastic nonlinear systems.
• The method successfully integrates fuzzy logic and backstepping for robust control design.
• The controller provides guaranteed stability and boundedness for the closed-loop system signals.