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