Applications of the Eigenvalue Theorem on Approximate Optimizations of Nonlinear Regulators

Abstract

A practical algorithm utilizing the theorem obtained in an eigenvalue analysis of nonlinear control is proposed. This theorem on the feedback optimization of nonlinear control systems by only one eigenfunction is enforced by an analytic continuation of the designer's constant H_R. Using this method of H_R=iH_R, typical Affine systems with 1-input and 2-states and with nonlinearities both in state equations of van-der-Pol type and in nonquadratic cost functions are optimized by feedback input. Accordingly, this report presents an algorithm to apply the eigenvalue theorem on the feedback optimization of nonlinear control systems.