About non-parametric identification of partial-parametred discrete-continuous process

The paper considers a new class of models under conditions of incomplete information. We are talking about multidimensional discrete-continuous processes for the case where the components of the vector of output variables are stochastically dependent. The nature of this dependence is a priori unknown, but for some channels the a priori information corresponds to both nonparametric and parametric type of the initial data in the process under study. Such a situation leads to a system of nonlinear equations, some of which will be unknown, while others are known accurate to the vector of parameters. The main purpose of the model is to determine the forecast of output variables with known input, and for implicit nonlinear equations it is only known that one or another component of the output depends on other variables that determine the state of the object. Thus, a rather nontrivial situation arises when solving a system of implicit nonlinear equations under conditions where in one channel of a multidimensional system equations themselves are not in the usual sense, while in others they are known up to parameters. Therefore, an object model cannot be constructed using the methods of the existing identi- fication theory as a result of a lack of a priori information. If it was possible to parameterize the system of nonlinear equations, then with a known input this system should be solved, since it is known and the parameterization stage is over. However, in this case it is still necessary to evaluate parameters. The main content of this article is the solution of the identification problem in the presence of a partially-parameterized discrete-continuous process, despite the fact that the parameterization stage cannot be overcome without additional a priori information on the process under study. In this regard, the scheme for solving the system of nonlinear equations can be represented as a certain sequential algorithmic chain. First, on the basis of the available training sample, including all components of the input and output variables observation, a residual vector is formed. After that, an estimate of the object output with known values of the input variables is constructed based on the estimates of Nadarai-Watson. Thus, for given values of the input variables of such a process, it is proposed to carry out a procedure for evaluating the forecast of output variables in accordance with the developed algorithmic chain. Numerous computational experiments, studying the proposed models of partially-parameterized discrete-continuous processes have shown their rather high efficiency. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology for predicting values of output variables from known input variables.