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

Necessary conditions for optimal open-loop strategies

verfasst von: M. H. Breitner, H. J. Pesch, W. Grimm
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.
Externe Organisation(en): Technische Universität München (TUM)
Universität Stuttgart
Typ: Artikel
Journal: Journal of Optimization Theory and Applications
Band: 78
Seiten: 419-441
Anzahl der Seiten: 23
ISSN: 0022-3239
Publikationsdatum: 09.1993
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Steuerung und Optimierung, Managementlehre und Operations Resarch, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1007/BF00939876 (Zugang: Unbekannt)

BibTeX

@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",
}