Observer-based control for nonlinear parameter-varying systems: A sum-of-squares approach

Area of Science:

• Control Theory
• Nonlinear Systems Analysis
• System Identification

Background:

• Nonlinear parameter-varying (NPV) systems present significant control challenges.
• Observer-based controllers are crucial for estimating system states in the presence of uncertainties.
• Existing methods often involve complex iterative procedures and struggle with input constraints.

Purpose of the Study:

• To develop a novel observer-based controller design for nonlinear and time-varying systems.
• To address systems with and without input constraints.
• To simplify the design process and reduce computational complexity.

Main Methods:

• Utilizing Lyapunov stability theory to derive state-and-parameter-dependent linear matrix inequality (LMI) conditions.
• Formulating LMIs as convex programming problems solvable via sum-of-squares (SOS) techniques.
• Enabling independent design of the observer and state-feedback controller.

Main Results:

• Successfully derived LMI conditions for observer-based controller design.
• Avoided computationally intensive backstepping/iterative methods.
• Eliminated bilinear product terms, simplifying the controller structure.
• Demonstrated independent design of observer and controller, reducing complexity.

Conclusions:

• The proposed method offers a computationally efficient approach to designing controllers for nonlinear parameter-varying systems.
• The independent design of observer and controller is a key advantage.
• Simulation results validate the feasibility and effectiveness of the presented technique.