Optimal-control theory applied to a probabilistic intercept problem

The method of dynamic programming is applied to the problem of the optimum guidance of an interceptor designed to intercept a target capable of random maneuvers. A cost is associated with any final miss distance and with the interceptor maneuvers, and, because of the randomness of the target motion, the cost is also a random variable. By assuming that the cost components are quadratic functions of their arguments and by utilizing the ensemble average of the cost, a relatively simple closed-form expression for the control and for the average cost is obtained. It is found that the optimum system is stable and well damped, and that the effect of the random maneuvers is relatively small.