One-parameter optimal correction problem for the trajectory of an aerial vehicle with respect to the probability criterion

Abstract

The correction problem of an aerial vehicle trajectory is considered. The mathematical model of the correction process is represented by a scalar stochastic control system with a probability terminal performance index. The system’s state variable is the predicted miss of a single parameter of the aerial vehicle. It is assumed that the complete information about the state variable is available. The aim of the correction is to maximize the probability that the terminal miss does not exceed the prescribed level. The execution errors of the designed correction impulse are distributed uniformly. Using dynamic programming, a procedure for the optimization of corrections of the aerial vehicle trajectory with respect to the probability performance index is developed, and this procedure is used to solve the one-parameter optimal correction problem for the aerial vehicle for the case of N time steps. The resulting optimal control is compared to the known optimal controls with respect to other performance indices.