Algorithm for Noisy Function Minimization for Use in Determining Optimal Trajectories

摘要

This work concerns a technique to be used in the solution of optimal trajectory problems associated with kinetic energy weapons. In this problem, it is desired to solve for a control function (which might be thrust magnitude and direction of gimbaled engine) in time in order to minimize time to intercept an enemy missile. Such problems are really infinite dimensional in nature (i.e., determining the control at each time point along the trajectory). However, in using a digital computer to solve such problems, certain operations occur which make the problem discrete and so viewable in a finite dimensional setting. For example, to numerically integrate the differential equations of motion, only values of thrust at a finite number of time points (typically, the beginning of each integration interval) affect the trajectory. The problem then is to determine these values so as to minimize the time to intercept. For any particular trajectory, this quantity is computed through a complicated flight equation simulation model. Also inherent in this computation is noise so that the computed time to intercept is really a noisy quantity. The current algorithm considers the noise in solving for the optimal control.