Convergent dynamics of optimal nonlinear damping control

TL;DR

This paper analyzes the convergent behavior of an optimal nonlinear damping control for second-order systems, demonstrating global stability and unique limit solutions, supported by numerical examples.

Contribution

It establishes the convergence properties and stability of the proposed control method within Demidovich's framework for second-order systems.

Findings

Solutions are globally uniformly asymptotically stable.

Unique limit solutions exist at the origin.

Numerical examples confirm theoretical analysis.

Abstract

Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all solutions of the control system are globally uniformly asymptotically stable. The existence of the unique limit solution in the origin of the control error and its time derivative coordinates are shown in the sense of Demidovich's convergent dynamics. Explanative numerical examples are also provided along with analysis.