H_∞ Codesign for Uncertain Nonlinear Control Systems Based on Policy Iteration Method.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Optimization Theory

Background:

• Investigates H-infinity (H∞) codesign for nonlinear control systems facing unmatched uncertainties and adjustable parameters.
• Addresses the challenge of simultaneously solving for adjustable parameters and the H∞ controller to improve robust control performance.

Purpose of the Study:

• To develop a novel approach for H-infinity (H∞) codesign in nonlinear systems.
• To achieve superior robust control performance by jointly optimizing system parameters and the controller.
• To transform the complex Hamilton-Jacobi-Isaacs equation into a solvable optimization problem.

Main Methods:

• Introduced a bounded function and a specialized cost function to reformulate the problem.
• Transformed the Hamilton-Jacobi-Isaacs equation into an optimization problem with nonlinear inequality constraints.
• Proposed a novel policy iteration algorithm utilizing the sum of squares technique.
• Developed a modified algorithm to optimize the robust performance index.

Main Results:

• Successfully transformed the H-infinity (H∞) codesign problem into an optimization framework.
• Developed and validated a novel policy iteration algorithm for solving the codesign problem.
• Demonstrated convergence and performance improvement of the proposed algorithms through simulations.
• Provided a method for simultaneous optimization of adjustable parameters and H∞ controllers.

Conclusions:

• The proposed algorithms effectively address the H-infinity (H∞) codesign problem for nonlinear systems with unmatched uncertainties.
• The simultaneous optimization approach leads to significant improvements in robust control performance.
• The sum of squares technique and policy iteration provide a viable solution for complex control design problems.