A Newton-type method and optimality test for problems with bang-singular-bang optimal control

  • In the paper, a second-order method is investigated for control problems where the control has bang-singular-bang structure. To start with, the first-order system is formulated as a variational inequality including a differential equation for the switching function. For this system, a certain inexact Josephy-Newton method is considered. Under strong second-order sufficient conditions obtained via Goh's transformation of control and state-adjoint data, the local solvability is proved for the iterative problems. For so-called semilinear problems, locally the state and adjoint iterates converge superlinearly. The paper is completed by a Riccati test approach for verifying second-order optimality.

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Metadaten
Author: Ursula Felgenhauer
URL:http://www.ybook.co.jp/online2/oppafa/vol1/p197.html
Title of the source (English):Pure and Applied Functional Analysis
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2016
Tag:Bang-singular-bang control; Josephy--Newton method; Riccati equation; maximum principle; second-order conditions
Volume/Year:1
Issue number:2
First Page:197
Last Page:215
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
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