About the control of objects with the memory in a nonparametric uncertainty

We consider the problem of identification and control of stochastic objects with discrete - continuous nature of the process. In this paper, we study more general class of dynamic objects in the future - objects with memory. The characteristic distinguishing feature of these processes is the fact that in the description the difference analogues of differential equations, taken in the classical theory of identification and control, are not used. The similar processes occur in many different kennels control of aerospace technology. For example, when vibration testing spacecraft channel “vibrator-sensor mounted on the spacecraft” can be described by difference equations. In this case, the lack of natural analogy between the equation in continuous time and difference is typical. This feature is the main difference with memory objects from the traditional dynamic processes. It leaves its mark in the modeling and management of such objects, and determines the urgency of the problem. This article discusses theoretical information about nonparametric algorithms of identification and control. Non-parametric model for objects with memory addresses are considered in two embodiments. One of them is closely related with the description of the object as the Duhamel integral. The second way is partial parameterization of the object, that is, to meet the conditions of both parametric and non-parametric uncertainties. The constructing nonparametric algorithms of dual control are based on the idea of A. A. Feldbaum. It states that the input object “on” its inverse counterpart, the language of mathematicians its inverse. Obviously, the description may not be accurate for some reasons, and then the inverse operator can only approximately describe the process in the direction of “exit-entry”. On this basis, both non-parametric models of objects with memory and nonparametric algorithms of dual control are lined up. The learning system of dual control with active accumulation of information is carefully analyzed. The detailed results of the numerical investigation of non-parametric models for multivariate processes with memory, as well as the results of numerical experiments applying the algorithm of nonparametric adaptive dual control are given.