Adaptive Global Asymptotic Output Stabilization of Uncertain Nonlinear Systems Under Dynamic State/Input Quantization

Area of Science:

• Control Engineering
• Nonlinear Systems Theory
• Signal Processing

Background:

• Nonlinear systems often face challenges with uncertainties and quantization effects.
• Existing control strategies may offer limited stability guarantees (e.g., semi-global) or weaker convergence properties (e.g., ultimate boundedness).
• State and input quantization introduce significant hurdles in control design due to non-smoothness.

Purpose of the Study:

• To develop a novel adaptive backstepping control strategy for nonlinear systems with mismatched uncertainties.
• To address challenges posed by dynamic input and state quantization.
• To achieve global asymptotic convergence of the system output to the origin.

Main Methods:

• A novel adaptive backstepping control algorithm is proposed.
• A dual-channel dynamic quantization mechanism is implemented for adaptive parameter adjustment.
• Higher-order filters are designed to generate smooth, differentiable state estimates.
• Explicit guidelines for control parameter tuning are provided.

Main Results:

• The proposed strategy guarantees global asymptotic stability, an improvement over semi-global stability in prior work.
• The system output converges asymptotically to the origin, offering stronger performance than ultimate uniform boundedness.
• The dual-channel dynamic quantization mechanism allows for online adaptation of quantization parameters.
• Higher-order filters effectively resolve the nondifferentiability issues caused by state quantization.

Conclusions:

• The novel adaptive backstepping control strategy effectively handles nonlinear systems with mismatched uncertainties and quantization.
• The approach provides global asymptotic convergence and robust performance.
• Numerical simulations confirm the effectiveness and advantages of the proposed quantized control method.