Complex Diierential Games of Pursuit-evasion Type with State Constraints, Part 1: Necessary Conditions for Optimal Open-loop Strategies

B Abstract. Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the rst 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 nonsmooth data are discussed in detail. These conditions lead to multipoint boundary-value problems which can be solved very eeciently 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 ring 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.