Optimal interception with time constraint

This paper considers the problem of minimum-fuel interception with time constraint. The maneuver consists of using impulsive thrust to bring the interceptor from its initial orbit into a collision course with a target which is moving on a well-defined trajectory. The intercept time is either prescribed or is restricted to be less than an upper limit. The necessary conditions and the transversality conditions for optimality are discussed. The method of solution amounts to first solving a set of equations to obtain the primer vector for an initial one-impulse solution. Then, based on the information provided by the primer vector, rules are established to search for the optimal solution if the initial one-impulse trajectory is not optimal. The method is general, in the sense that it allows for solving the problem of three-dimensional interception with arbitrary motion for the target. Several numerical examples are presented, including orbital interceptions and interception at hyperbolic speeds of a ballistic missile.