Non-parametric identification and control algorithms for T-processes

In this paper, we consider nonparametric identification and control methods for multidimensional discrete-continuous processes with delay, which are typical for many real industries. Of course, such systems are typical for practice, including in the rocket and space industry, as well as in technological processes for the production of space technology. In multidimensional processes, we must take into account the relationships between input and output variables, as well as their relationship with each other. Moreover, these connections are not always known to the researcher. Taking into account the unknown connections of the input variables, the researcher will deal with tubular processes or H-models, and if the unknown connections of the output variables are taken into account, the model along one or another channel of the object will be analogs of implicit functions. In general, the model of a multidimensional object will be represented as a system of nonlinear implicit equations. In this case, the solution to the identification problem will be reduced to finding the forecast of the vector of output variables from the known values of the vector of input variables and can be obtained only as a result of solving the corresponding system of equations, which were called T-models, which will be discussed in this article. The solution of a system of nonlinear implicit equations by parametric identification methods will not lead to the desired result, due to the lack of sufficient a priori information, this is where the need to use nonparametric identification methods arises, as well as the necessary use of system analysis methods. A priori information in problems of nonparametric statistics is insufficient, which cannot be dealt with by generally accepted identification methods.

When managing multidimensional processes, the dependencies of the output variables should be taken into account. Here another important feature arises, which consists in the fact that random values from the range of definition of output variables cannot be used as reference influences, they must be selected from their common intersection.