Mathematics & Physics 2016, 9(3), 338–346 УДК 519.21 Mathematical Modeling of H-processes Alexander V.Medvedev∗ Siberian State Aerospace University Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660014 Russia Eugene D.Mihov† Oleg V.Nepomnyashchiy‡ Institute of Space and Information Technology Siberian Federal University Kirensky, 26, Krasnoyarsk, 660074 Russia Received 27.01.2016, received in revised form 16.04.2016, accepted 22.06.2016 The problem of the discrete continuous processes having "tubular" structure in space "input-output" variables’s modeling is investigated. <...> The fact that when the trained parametrical models of "tubular" processes’s creating, it’s important to use corresponding nonparametric indicators, is reflected. <...> This examples proves that "tubular" processes proceed in the space of fractional dimension. <...> Introduction Identification of stochastic objects is often reduced to the identification of static systems with delay. <...> This is due to the fact that some output variables of the object are controlled for much longer time than the input variables. <...> For example, several variables are measured electrically (in this case, the discrete control can be brief) but the other variables are controlled by chemical analysis or physical-mechanical tests (in this case the discrete control ∆T is long, i.e. ∆T ≫∆t). <...> The most common scheme of a discrete-continuous process is shown in Fig. 1: The notation of Fig. 1: A is the investigate object (the process); − − x→(t), − − output vectors of the process; − variable; − − measured input vector of i-th process; − ξ→(t) is the casual influence; − − u→(t) is the vector of control actions; − − −− − q→(t) and − − z→(t) are the − µ→(t) is the uncontrolled but λ→(t) is the input vector of unmanaged and measured process ω →i(t) : i = 1, k are the process variables controlled in object; t is time; Hµ,Hu,Hx,Hz,Hq,Hω are the communication channels corresponding to various variables, including control devices and devices for measurement of observed variables; µt,ut,xt,ωt are measurements of − µ→(t),−− u→(t),−− x→(t),−− ω→(t) at time moment t; hµ(t),hu(t),hx(t <...>