Modal approach to the controllability problem of distributed parameter systems with damping

TL;DR

This paper investigates the controllability of damped distributed parameter systems using modal analysis and minimum energy controls, providing conditions for approximate controllability in flexible structures.

Contribution

It introduces a modal approach with minimum energy controls to analyze controllability of damped distributed systems, offering new sufficient conditions.

Findings

Established approximate controllability conditions for damped systems

Utilized modal representation for flexible structures

Proposed a method for infinite-dimensional steering problems

Abstract

This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional steering problem approximately. Sufficient conditions of the approximate controllability are formulated for a modal representation of a flexible structure with small damping.