Time-optimal rendezvous strategies

This paper is concerned with the control of two distinct
n
th-order linear systems described in the standard state vector notation. Since both systems are of
n
th order their state vectors can be placed in the same
n
-dimensional phase space. A problem is formulated in which it is desired to transfer each system from separate initial states to some undetermined but coincident state (state vector rendezvous). This goal is to be accomplished in minimum time while the input vectors of both systems are amplitude constrained. Complete necessary and sufficient conditions which must be satisfied by time-optimal solutions are developed, and additionally, a technique for computing the optimum controls is given.