Robust control of uncertain fully actuated systems with nonlinear uncertainties and perturbed input matrices

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics

Background:

• Robust control is crucial for systems with uncertainties.
• Existing methods for fully actuated systems (FASs) have limitations with nonlinear uncertainties and perturbed input matrices.
• Previous work on FASs faced constraints in handling certain types of input matrix perturbations.

Purpose of the Study:

• To develop novel robust controllers for uncertain fully actuated systems (FASs).
• To relax existing assumptions on system uncertainties and perturbed input matrices.
• To enhance the stability and performance of closed-loop systems under broader conditions.

Main Methods:

• Development of two novel robust controllers for two distinct cases.
• Relaxation of assumptions on the perturbation input matrix, accommodating a wider range of matrices.
• Further relaxation of system uncertainty assumptions for one case, leading to bounded states.
• Imposition of specific requirements on system nonlinearity for the second case, ensuring global exponential stability.

Main Results:

• The proposed controllers successfully handle a wider class of perturbed input matrices compared to previous methods.
• For the first case, closed-loop system states are globally bounded and converge to a small domain around the origin.
• For the second case, global exponential stability of the closed-loop system is achieved.
• The controllers demonstrated effectiveness when applied to an electromechanical system.

Conclusions:

• The developed robust controllers offer improved performance and broader applicability for uncertain fully actuated systems.
• The relaxed assumptions significantly expand the range of systems that can be effectively controlled.
• The methods provide robust solutions for nonlinear systems with significant uncertainties and input perturbations.