Optimal interception with time constraint
Abstract
This paper considers the problem of minimumfuel 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 welldefined 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 oneimpulse solution. Then, based on the information provided by the primer vector, rules are established to search for the optimal solution if the initial oneimpulse trajectory is not optimal. The method is general, in the sense that it allows for solving the problem of threedimensional interception with arbitrary motion for the target. Several numerical examples are presented, including orbital interceptions and interception at hyperbolic speeds of a ballistic missile.
 Publication:

Journal of Optimization Theory Applications
 Pub Date:
 September 1990
 Bibcode:
 1990JOTA...66..361V
 Keywords:

 Hodographs;
 Interception;
 Missile Trajectories;
 Orbit Transfer Vehicles;
 Spacecraft Maneuvers;
 Trajectory Optimization;
 Ballistic Missiles;
 Fuel Consumption;
 Optimization;
 Target Acquisition;
 Time Dependence;
 Astrodynamics