Minimum energy guidance for boost phase ballistic missile interception

Using as the optimality index the required energy for interception of a ballistic missile in its boost phase, it is shown that the cost has an absolute minimum for a finite interception duration. The problem of interception of a thrusting target has an optimal solution for a free final time. The required interceptor three dimensional acceleration vector for the interception of a ballistic missile in its boost phase is derived in feedback form. Time to go, the critical variable in all optimal guidance laws, is derived in closed form as the solution of a nonlinear algebraic equation. Closed loop implementation of the optimal guidance law is based on the current prediction of the target trajectory. Numerical results for a representative intercept are presented.