An Ensemble Averaging Approach to Optimal Guidance Polynomial Approximations

An approach to optimal guidance synthesis is developed in which an ensemble-averaged second order approximation to the performance function is minimized subject to constraints on the means and variances of other functions. The minimization is with respect to coefficients of assumed polynomial approximations of a linear feedback control law (in which the state is perfectly known) and coefficients in a linear termination law. A brief comparison is drawn with deterministic neighboring extremal control. While attention is directed mainly to first order necessary conditions, some comments are made on numerical solution by first and second order successive approximation methods. Extensions to include disturbances other than initial errors and to include state estimation errors are discussed briefly.