Necessary conditions for distributed optimal control of linearized compressible Navier-Stokes equations with state constraint

TL;DR

This paper derives necessary optimality conditions for controlling linearized compressible Navier-Stokes equations with constraints, using a Pontryagin maximum principle based on the Ekeland variational principle.

Contribution

It establishes an integral-type Pontryagin maximum principle for distributed control of constrained linearized compressible flows, extending optimal control theory to this complex setting.

Findings

Derived a Pontryagin maximum principle for the problem

Established conditions for optimal controls in constrained flows

Applied Ekeland variational principle to this control problem

Abstract

A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows is established using the Ekeland variational principle. The controls are distributed over a bounded domain, while the state variables are subject to a set of constraints and governed by the linearized compressible Navier-Stokes equations. The maximum principle is of integral-type and obtained for minimizers of a tracking-type integral cost functional.