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Complex differential games of pursuit-evasion type with state constraints. I: Necessary conditions for optimal open-loop strategies. (English) Zbl 0796.90078

Summary: 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 multipoint 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.

MSC:

91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
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