Observer-based robust control of one-sided Lipschitz nonlinear systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Optimization Theory

Background:

• Nonlinear systems are susceptible to time-varying parametric uncertainties and external disturbances.
• Designing controllers for such systems requires robust methodologies to ensure stability and performance.
• One-sided Lipschitz nonlinear systems present unique challenges in controller design.

Purpose of the Study:

• To develop an observer-based controller for nonlinear systems with parametric uncertainties and norm-bounded disturbances.
• To ensure robustness against L2-norm-bounded perturbations.
• To provide a numerically tractable and less conservative design approach.

Main Methods:

• Utilizing Young's inequality and matrix decompositions for controller gain extraction.
• Employing convex optimization conditions for simultaneous observer and controller gain determination.
• Applying a nonlinear iterative cone-complementary linearization method to handle constraints.

Main Results:

• A sufficient condition for observer and controller gain extraction was established.
• The proposed observer-based control technique demonstrates robustness against parametric uncertainties and L2-norm-bounded perturbations.
• Simulation examples validate the effectiveness of the developed methodologies.

Conclusions:

• The developed observer-based controller effectively manages nonlinear systems with uncertainties and disturbances.
• The methodology offers a robust and computationally tractable solution for complex control problems.
• The approach ensures reliable system performance in the presence of external perturbations.