Minimum Information Stochastic Modelling of Linear Systems with a Class of Parameter Uncertainies

This paper considers the problem of mean-square optimal control for a linear system with stochastic parameters and limited prior information. For specific application to flexible mechanical systems, consideration is limited to the class of multiplicative parameter perturbations of skew-hermitian type. To avoid ad hoc assumptions regarding a priori statistics, a prior probability assignment is induced from available data through use of a maximum entropy principle. Moreover, we discern a minimum set of a priori data which is just sufficient to induce a well-defined maximum entropy probability assignment. The statistical-description induced by this minimum data set is tantamount to a form of Stratonovich state-dependent noise.