Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Technische Universität München (TUM)
  • Universität Stuttgart
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)419-441
Seitenumfang23
FachzeitschriftJournal of Optimization Theory and Applications
Jahrgang78
Ausgabenummer3
PublikationsstatusVeröffentlicht - Sept. 1993
Extern publiziertJa

Abstract

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.

ASJC Scopus Sachgebiete

Zitieren

Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies. / Breitner, M. H.; Pesch, H. J.; Grimm, W.
in: Journal of Optimization Theory and Applications, Jahrgang 78, Nr. 3, 09.1993, S. 419-441.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Download
@article{73121ddf28844917b334aa82e4f66b51,
title = "Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies",
abstract = "Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.",
keywords = "barrier surface, Differential games, flight mechanics, missile firing range, multipoint boundary-value problems, open-loop strategies, pursuit-evasion games, singular surfaces, state constraints",
author = "Breitner, {M. H.} and Pesch, {H. J.} and W. Grimm",
note = "Copyright: Copyright 2007 Elsevier B.V., All rights reserved.",
year = "1993",
month = sep,
doi = "10.1007/BF00939876",
language = "English",
volume = "78",
pages = "419--441",
journal = "Journal of Optimization Theory and Applications",
issn = "0022-3239",
publisher = "Springer New York",
number = "3",

}

Download

TY - JOUR

T1 - Complex differential games of pursuit-evasion type with state constraints, part 1

T2 - Necessary conditions for optimal open-loop strategies

AU - Breitner, M. H.

AU - Pesch, H. J.

AU - Grimm, W.

N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.

PY - 1993/9

Y1 - 1993/9

N2 - Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.

AB - Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.

KW - barrier surface

KW - Differential games

KW - flight mechanics

KW - missile firing range

KW - multipoint boundary-value problems

KW - open-loop strategies

KW - pursuit-evasion games

KW - singular surfaces

KW - state constraints

UR - http://www.scopus.com/inward/record.url?scp=0027663086&partnerID=8YFLogxK

U2 - 10.1007/BF00939876

DO - 10.1007/BF00939876

M3 - Article

AN - SCOPUS:0027663086

VL - 78

SP - 419

EP - 441

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 3

ER -

Von denselben Autoren