Optimal codesign of nonlinear control systems based on a modified policy iteration method.

Area of Science:

• Control Systems Engineering
• Optimization Theory
• Nonlinear Dynamics

Background:

• Optimal codesign involves simultaneously designing physical plants and control policies.
• Nonlinearities can arise from nonquadratic cost functions or the plant itself.
• Existing methods may struggle with the nonconvex nature of nonlinear codesign problems.

Purpose of the Study:

• To develop an iterative methodology for the optimal codesign of nonlinear control systems.
• To rigorously prove performance improvements and convergence guarantees.
• To demonstrate the applicability to both nonlinear and linear systems.

Main Methods:

• Formulating the optimal codesign as a nonconvex optimization problem.
• Proposing an iterative scheme combining conventional policy iteration with system-equivalence-based policy improvement.
• Proving rigorous convergence and performance enhancement properties.
• Showing that the improvement step can be solved via quadratic programming under certain conditions.

Main Results:

• The proposed iterative scheme rigorously improves closed-loop system performance at each step.
• Convergence to a suboptimal solution is guaranteed.
• The additional policy improvement step can be efficiently solved using quadratic programming.
• The methodology is effective for the optimal codesign of a load-positioning system.

Conclusions:

• The presented iterative approach offers a robust method for nonlinear control systems optimal codesign.
• The technique ensures performance enhancement and convergence, applicable to various control system designs.
• The study validates the methodology through a practical example, highlighting its effectiveness.