Optimization of the proportional navigation law with time delay

The controlled relative motion of spacecraft nearby an orbital station is considered. The rendezvous method used at the active spacecraft is an algorithm of proportional navigation which is realized with some constant time delay. The coefficient of the law of guidance is considered to be the control variable, a step time function. The problem of choice of the mentioned coefficient which provides a minimum of the rendezvous time is analyzed. It turns out that the optimal solution includes both boundary and intermediate control values. The results of computer simulation are given.