Multicriteria method for identification and forecasting

The multicritera approach to identification and forecasting for mathematical models is considered. The need for such an approach arises, in particular, when it is required to take into account the errors that cannot be reduced to one function, and in the absence of specific information about the data interference class. Paper is devoted to the multicritera version of the Identification Sets Method based on approximation and visualization of the identification errors vector-function graph and its projections on identification parameters space. The nearness function for criterion point proximity to the set of nonimprovable (Pareto efficient) identification solutions is defined. The efficient criteria set, efficient and sub-efficient parameters sets and corresponding forecasting trajectories tubes are explored. To construct these objects we use methods for approximation of implicitly specified sets, in particular, methods for approximation the Edgeworth–Pareto hull and the deep holes method. The technique and examples for the case of two identification criteria are considered in detail.