Analysis of sufficiency of experimental and \textit{a priori} information in the identification problem of a dynamic system (Q1386979)

The condition of complete observability for dynamic systems with unknown coordinates is fairly artificial in the sense that it is not motivated by the physical meaning of a system and is not connected with our needs. Thus, if we are interested not in the whole set of coordinates and parameters of the system, but only in a small set of functions of those parameters, then it is appropriate to decrease the number of observable values and collected experimental information, since extra information requires extra measuring devices and extra equipment for the processing and storage of information. However, in this case, to deal with systems that are not completely observable, the traditional methods, which are elaborated for completely observable systems, are not appropriate. Thus, one must find an approach that allows one to minimize the experimental and a priori information, and to formulate the criterion, the test of values that can be determined by experimental data at our disposal, and that also allows one to vary (diminish) the set of observable values in such a way that the class of values admitting determinations corresponds to our problems. In this paper, the authors present a version of such an approach. A nonlinear, nonautonomous system not completely observed is studied by differential-geometric methods. For experimental data, a method for finding the complete independent part is proposed (in order to eliminate the extra part); also, a criterion characterizing the possibility to determine the values of an arbitrary functional of coordinates and parameters of the system by experimental data is found. For a priori information, a method of minimization up to mutually independent constants is proposed. A correspondence (in both directions) is found for arbitrary corrections of functions of coordinates and of system parameters, which is necessary for their determination by a priori information.