Obtaining Reduced-Order Stochastic Models

Recent approaches to stochastic model reduction have followed the balancing approach introduced by Moore for the deterministic model reduction problem. In this approach, a given model is transformed to one in which the state variables are ordered with respect to their contribution to some criterion, and the reduced-order model is then obtained by deleting the least important variables. In the deterministic case, the ordering of the state variable implies that the reduced-order model is a subsystem of the original model. However, this is not necessarily true in the stochastic case. In this paper, an optimality framework for obtaining reduced-order stochastic models is derived. Since exact solutions appear intractable, a new suboptimal approach is presented.