Convergent dynamics of optimal nonlinear damping control

Abstract

Following the Demidovich’s concept and definition of convergent systems, we analyze the optimal nonlinear damping control which was recently proposed for the second-order systems. Targeting the problem of servo-regulation, and more specifically output tracking of the C1 reference trajectories, it is shown that all solutions of the proposed control system are globally uniformly asymptotically stable. The existence of the unique limit solution in the coordinates origin of the control error and its time derivative are shown in the sense Demidovich’s convergent dynamics. Explanatory numerical examples are provided to accompany the analysis.