On practical application of Zubov’s optimal damping concept

Abstract

This article presents some new ideas connected to nonlinear and nonautonomous control laws based on the application of an optimization approach. There is an essential connection between practical demands and the functionals to be minimized. This connection is at the heart of the proposed methods. The discussion is focused on the optimal damping concept first proposed by V. I. Zubov in the early 1960’s. Significant attention is paid to various modern aspects of the optimal damping theory’s practical implementation. Emphasis is given to the specific choice of the functional to be damped to provide the desirable stability and performance features of a closed-loop system. The applicability and effectiveness of the proposed approach are confirmed by an illustrative numerical example.