Approximate and exact controllability criteria for linear one-dimensional hyperbolic systems

TL;DR

This paper establishes criteria for controllability of linear one-dimensional hyperbolic systems using frequency domain analysis, with applications to network flows, advancing understanding of control in infinite-dimensional systems.

Contribution

It provides necessary and sufficient controllability conditions for hyperbolic systems via infinite-dimensional realization theory and frequency domain methods, a novel approach in this context.

Findings

Derived controllability criteria in the frequency domain.

Applied results to network flow systems.

Established conditions for both approximate and exact controllability.

Abstract

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary and sufficient conditions for approximate and exact controllability, expressed in the frequency domain. The results are applied to flows in networks.