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.


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


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