Adaptive backstepping quantized control for a class of unknown nonlinear systems

Area of Science:

• Control Theory
• Nonlinear Systems Analysis
• Systems Engineering

Background:

• Nonlinear systems with strict-feedback structures are challenging to control, especially with input quantization.
• Input quantization can introduce uncertainties and chattering, complicating stability analysis.
• Existing methods often require global Lipschitz assumptions or struggle with quantization errors.

Purpose of the Study:

• To develop a robust control scheme for uncertain nonlinear systems with input quantization.
• To address the stability problem by effectively managing quantization errors.
• To eliminate restrictive assumptions and design parameters found in prior work.

Main Methods:

• Utilizing a sector-bounded hysteresis quantizer to achieve signal quantization and reduce chattering.
• Employing a common Lyapunov function (CLF) and the backstepping method for control design.
• Directly incorporating sector-bounding features to handle quantization error without decomposition.

Main Results:

• The proposed control scheme guarantees asymptotic stability of system trajectories to the origin.
• The method successfully avoids the need for global Lipschitz assumptions on system nonlinearities.
• Restrictions on quantization design parameters, such as quantization density, are eliminated.

Conclusions:

• The developed control strategy provides a more general and less restrictive approach to stabilizing nonlinear systems with input quantization.
• The technique effectively manages quantization errors, ensuring system stability and performance.
• Simulation results validate the accuracy and efficiency of the proposed control scheme.