Variational maximum principle in controlled systems of one-dimensional hyperbolic equations
type: Item
instance of: scholarly article
title: Variational maximum principle in controlled systems of one-dimensional hyperbolic equations
zbMATH Open document ID: 0993.49021
published in: Russian Mathematics
publication date: 2001-03-07T00:00:00Z
review text: The paper considers optimal control problems for the semilinear hyperbolic system \[ z_t+ A(x, t)z_x= f(x,t,z,u)\tag{1} \] in a rectangle \(D= \{(x, t)\in\mathbb{R}^2\mid 0< x< a, 0< t< T\}\). The cost functional is standard and includes an additional integral along a line \(\{(x, t)\mid x= x_0, 0< t< T\}\) with \(x_0\subset (0,a)\). The author gives short proofs for the Pontryagin's maximum principle and its analogue along characteristics of (1).
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35J50
zbMATH DE Number: 1541557
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: optimal control
zbMATH Keywords: semilinear hyperbolic system
zbMATH Keywords: Pontryagin's maximum principle
author: Viktor Anatol'evich Terletskiĭ
reviewed by: Uldis Raitums
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1541557