Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints

Stefan Doboszczak; Manil T. Mohan; Sivaguru S. Sritharan

doi:10.3934/eect.2020110

Article Contents

2022, Volume 11, Issue 2: 347-371. Doi: 10.3934/eect.2020110

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Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints

1.
Department of Mathematics, University of Maryland, College Park, MD 20740, USA
2.
Department of Mathematics, Indian Institute of Technology Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India
3.
M. S. Ramaiah University of Applied Sciences, University House, New BEL Road, MSR Nagar, Bangalore-560 054a, India

^*Corresponding author: doboss27@umd.edu
^*Corresponding author: doboss27@umd.edu

Received: August 31, 2020

Revised: August 31, 2020

Early access: December 2020

Published: April 2022

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Abstract

A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows subject to state constraints is established using the Ekeland variational principle. Since the system considered here is of coupled parabolic-hyperbolic type, the well developed control theory literature using abstract semigroup approach to linear and semilinear partial differential equations does not seem to contain problems of the type studied in this paper. The controls are distributed over a bounded domain, while the state variables are subject to a set of constraints and governed by the compressible Navier-Stokes equations linearized around a suitably regular base state. The maximum principle is of integral-type and obtained for minimizers of a tracking-type integral cost functional.

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Mathematics Subject Classification: Primary: 49K20, 76N25; Secondary: 49J20, 35Q30.

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