Asymptotic State Regulation of Fully Actuated Systems With Time-Varying Parameters and Perturbed Input Matrices

Area of Science:

• Control Theory
• Systems Engineering
• Robotics

Background:

• Fully actuated systems (FASs) often face challenges due to time-varying parameters and uncertainties.
• Existing methods for FASs with time-varying parameters typically require differentiability, limiting their applicability.
• Previous control strategies often achieved global boundedness rather than asymptotic convergence of state variables.

Purpose of the Study:

• To develop a robust adaptive control method for FASs with time-varying unknown parameters, perturbed input matrices, and nonlinear uncertainties.
• To overcome the limitations of existing methods by removing the differentiability requirement for time-varying parameters.
• To achieve global asymptotic convergence of state variables and global boundedness of parameter estimation.

Main Methods:

• A novel robust adaptive control strategy inspired by the congelation of variables method is proposed.
• The controller integrates an adaptive component for parameter compensation and a robust component for handling uncertainties.
• The method is extended to disturbed systems, and parameter selection is discussed.

Main Results:

• The proposed method successfully handles continuous, bounded, but non-differentiable time-varying parameters.
• Global asymptotic convergence of state variables is achieved, surpassing previous global boundedness results.
• Global boundedness of the parameter estimation is guaranteed.

Conclusions:

• The novel robust adaptive method offers a more general and effective approach for controlling FASs with complex uncertainties.
• The method's ability to handle non-differentiable parameters expands its practical applicability.
• Successful application to resonant circuit and ship steering systems demonstrates its effectiveness.