Regularity of the steering control for systems with persistent memory

TL;DR

This paper extends the regularity properties of steering controls to systems with persistent memory, providing a variational characterization that could enhance numerical methods for control computation.

Contribution

It introduces a regularity result for systems with Maxwell/Boltzmann type memory and offers a variational framework for smooth steering control.

Findings

Established regularity of steering controls for systems with persistent memory.

Provided a variational characterization of the smooth steering control.

Potentially enables improved numerical algorithms for control synthesis.

Abstract

The following fact is known for large classes of distributed control systems: when the target is regular, there exists a regular steering control. This fact is important to prove convergence estimates of numerical algorithms for the approximate computation of the steering control. In this paper we extend this property to a class of systems with persistent memory (of Maxwell/Boltzmann type) and we give a variational characterization of the smooth steering control which may open the way to an extension of the numerical approach proposed by Ervedoza and Zuazua.