Details
| Original language | English |
|---|---|
| Pages (from-to) | 419-441 |
| Number of pages | 23 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 78 |
| Issue number | 3 |
| Publication status | Published - Sept 1993 |
| Externally published | Yes |
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
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Decision Sciences(all)
- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics
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In: Journal of Optimization Theory and Applications, Vol. 78, No. 3, 09.1993, p. 419-441.
Research output: Contribution to journal › Article › Research › peer review
}
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 -