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We consider optimal two-impulse space interception problems withmulti-constraints. The multi-constraints are imposed on the terminal positionof an interceptor, impulse and impact instants, and the component-wisemagnitudes of velocity impulses. We formulate these optimization problems asmulti-point boundary value problems and the calculus of variations is used tosolve them. All inequality constraints are converted into equality constraintsby using slackness variable methods in order to use Lagrange multiplier method.A new dynamic slackness variable method is presented. As a result, an indirectoptimization method is established for two-impulse space interception problemswith multi-constraints. Subsequently, our method is used to solve thetwo-impulse space interception problems of free-flight ballistic missiles. Anumber of conclusions have been established based on highly accurate numericalsolutions. Specifically, by numerical examples, we show that when time andvelocity impulse constraints are imposed, optimal two-impulse solutions mayoccur, and also if two impulse instants are free, then two-impulse spaceinterception problems with velocity impulse constraints may degenerate to theone-impulse case.

Optimal Two-impulse Space Interception with Multi-constraints