Maximum principle of state-constrained optimal control governed by fluid dynamic systems
type: Item
instance of: scholarly article
title: Maximum principle of state-constrained optimal control governed by fluid dynamic systems
zbMATH Open document ID: 1032.49033
DOI: 10.1016/S0362-546X(02)00282-1
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-02T00:00:00Z
review text: This work is concerned with optimal control of systems governed by three-dimensional Navier-Stokes equations which are non-well-posed, and the state constraint is of integral form. The authors define a penalty functional, via which they transform the original problem with the state constraint into another one called the approximate problem, which has no state constraint. Then they apply Ekeland's variational principle to find an optimal control pair for the approximate problem. By using the spike variation, they derive first-order necessary conditions for the optimal pair of the approximate problem; passing to the limit they obtain necessary conditions for the original optimal pair.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 76D55
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1891305
zbMATH Keywords: optimal control
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: state constraint
zbMATH Keywords: non-well-posed equation
zbMATH Keywords: Ekeland's variational principle
author: Gengsheng Wang
author: Lijuan Wang
reviewed by: Hussain A. El-Saify
MaRDI profile type: Publication
cites work: Topological methods in hydrodynamics
cites work: Q4094029
cites work: Analysis and control of nonlinear infinite dimensional systems
cites work: The time optimal control of Navier-Stokes equations
cites work: Optimal control of Navier-Stokes equations with periodic inputs
cites work: Flow invariance preserving feedback controllers for the Navier-Stokes equation.
cites work: Necessary and sufficient conditions for optimal controls in viscous flow problems
cites work: Q3935753
cites work: Q4936365
cites work: Necessary Conditions for Optimal Control of Distributed Parameter Systems
cites work: Q5601627
cites work: Q4303526
cites work: Q4192429
cites work: Optimal Controls of 3-Dimensional Navier--Stokes Equations with State Constraints
cites work: Pontryagin maximum principle of optimal control governed by fluid dynamic systems with two point boundary state constraint
description: scientific article; zbMATH DE number 1891305