Stochastic model simplification

Mathematical models, defined by a structure and a set of parameter variation or uncertainty, may, be simplified both by structure reduction and parameter set reduction. First, the approximation of high-order and time varying linear Gaussian models by low-order and time-invariant ones is considered. The proposed approach is based on maximizing the probabilistic ambiguity between the actual model and the approximate one, and is applicable to general stochastic linear models. Reducing a model set, defined on a set of parameter variation or uncertainty, to a single fixed parameter model or a finite model group, is then considered. The set reduction criteria give rise to a min-max optimization problem and a min-max-min problem, which is converted to a constrained min-max problem. The algorithmic solution of the optimization problems is considered in detail, along with several approximation and discretization schemes. The application and the validity, of the proposed approach are examined in view of traditional design considerations by solving numerical examples for several structure and set reduction problems.