Exact Controllability of the Distributed System Governed by the Wave Equation with Memory

TL;DR

This paper proves that a wave equation with memory, modeled as a distributed system, can be exactly controlled to reach rest in finite time with bounded control, when the memory kernel is a sum of exponentials.

Contribution

It establishes the exact controllability of wave equations with memory kernels expressed as linear combinations of exponentials, extending control theory to systems with memory effects.

Findings

System can be driven to rest in finite time

Control function remains bounded

Memory kernel is a linear combination of exponentials

Abstract

We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control function being bounded. In this case the memory kernel is a linear combination of exponentials.