Practical Stochastic Optimal Guidance Law for Bounded Acceleration Missiles

The purpose of this paper is to develop an optimal guidance law that takes into account both the missile acceleration limit and a maximum value allowed for the guidance gain. The maximum value of the guidance gain is dictated mainly by the possible coupling between the missile body motions and the measurement of the inertial target line-of-sight angle rate. The tools for this work are the linear quadratic stochastic Gaussian optimal control theory coupled with the use of random-input describing functions. Although the use of the random-input describing function introduces an approximation in the work, it has been shown in the past that the use of random-input describing functions in miss distance calculations results in good approximations for the predicted miss distance. The paper includes the derivation of the optimal guidance law that accounts for both the missile acceleration limit and the constraint on the guidance gain and a simple one-dimensional Monte Carlo simulation to examine the performance of the guidance law.