Modeling and Optimal Control of Networks of Pipes and Canals

TL;DR

This paper develops a mathematical framework for the optimal control of complex network systems like pipelines and channels, proving the existence of optimal solutions using advanced analytical techniques.

Contribution

It introduces a novel approach to control systems governed by nonlinear conservation laws at junctions, with rigorous existence proofs.

Findings

Existence of optimal control solutions established

Applicable to gas pipelines and open channels

Uses quasidifferential equations in metric spaces

Abstract

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an optimal control is proved. From the analytical point of view, these results are based on the well posedness of a suitable initial boundary value problem and on techniques for quasidifferential equations in a metric space.