Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.17223/19988605/53/7
Ключевые слова: nonparametric modeling, control, inertialess systems, t-processes, t-models, algorithm chain
Аннотация: The work is devoted to the problems of nonparametric identification and control of multidimensional discrete-continuous processes. Discrete-continuous processes occur continuously in space, but their variables are monitored at discrete time instants. Such processes are considered as inertialess with delay. This is explained by the Показать полностьюfact that, through various channels of a multidimensional system, the measurement of output variables is carried out at different time intervals. Examples of such processes can be the processes of the mining or processing industries, in particular, in the construction industry (cement production process), metallurgy (steel smelting process), oil refining (diesel hydrotreatment process) and many others If the output variables of a multidimensional object are somehow stochastically dependent, and this dependence is unknown, then such processes were called T-processes. Such processes require a special look at the identification problem, which is somewhat different from the generally accepted ones. The main thing here is that the identification of such objects should be carried out in a way that is not traditional for the existing theory of identification. This emphasizes the importance of the identification problem for many real-life processes of discrete-continuous nature. A feature of such processes is that the vector of output variables , consisting of n components, is such that the components of this vector are stochastically dependent in an unknown manner. Denote the vector of input components by Such a formulation of the question leads to the fact that the mathematical description of the object can be represented in the form of some system of implicit functions of the form F u t x t.j.n. The main feature of this modeling problem is that the class of dependencies is a priori unknown, due to a lack of a priori information. That is, there is no parametric class of vector functions F u t x t. j. n, where a is a vector of parameters, which does not allow the use of parametric identification methods, because the class of functions cannot be determined a priori and the known identification methods are not suitable. As a result of the above, the identification problem is reduced to the problem of solving a system of nonlinear equations with respect to the components of the vector nx t. x t x t x t, for known values of mu t. u t u t u t. A situation arises when it is necessary to solve a system of interrelated equations, but this system is not defined. In this case, it is possible to use a sequential chain of algorithms to find the values of the components of the vector of output variables x. t. from the known input u.t The task of controlling a discrete-continuous process is considered under conditions of nonparametric uncertainty, that is, when the object in question is not described up to the parameter vector a. In this case, it is advisable to use a chain of control algorithms to search for the corresponding control action u(t) at each step. If the dimension of the input vector..ut exceeds the dimension of the output vectorxt, then some of the components of the input variables..ut can be interpreted as uncontrolled, but controlled. This often corresponds to actual technological processes. We have carried out numerous computational experiments on the identification and control of T-processes, which have shown a fairly high efficiency. The article presents some fragments of numerical studies. In this case, options were considered with different dimensionalities of objects, the level of interference, the volume of training samples, and others. The work is devoted to the problems of nonparametric identification and control of multidimensional discrete-continuous processes. Discrete-continuous processes occur continuously in space, but their variables are monitored at discrete time instants. Such processes are considered as inertialess with delay. This is explained by the fact that, through various channels of a multidimensional system, the measurement of output variables is carried out at different time intervals. Examples of such processes can be the processes of the mining or processing industries, in particular, in the construction industry (cement production process), metallurgy (steel smelting process), oil refining (diesel hydrotreatment process) and many others If the output variables of a multidimensional object are somehow stochastically dependent, and this dependence is unknown, then such processes were called T-processes. Such processes require a special look at the identification problem, which is somewhat different from the generally accepted ones. The main thing here is that the identification of such objects should be carried out in a way that is not traditional for the existing theory of identification. This emphasizes the importance of the identification problem for many real-life processes of discrete-continuous nature. A feature of such processes is that the vector of output variables x(t) = (x1 (t), x2 (t),..., xn (t)), j = 1, n, consisting of n components, is such that the components of this vector are stochastically dependent in an unknown manner. Denote the vector of input components by u (t) = (u1 (t), u2 (t),...,um (t)), k = 1, m. Such a formulation of the question leads to the fact that the mathematical description of the object can be represented in the form of some system of implicit functions of the form Fj (u (t), x(t)) = 0, j = 1, n. The main feature of this modeling problem is that the class of dependencies F (.) is a priori unknown, due to a lack of a priori information. That is, there is no parametric class of vector functions Fj (u (t), x (t), α), j = 1, n, where α is a vector of parameters, which does not allow the use of parametric identification methods, because the class of functions cannot be determined a priori and the known identification methods are not suitable. As a result of the above, the identification problem is reduced to the problem of solving a system of nonlinear equations Fj (u (t), x (t), α), j = 1, n with respect to the components of the vector x(t) = (x1 (t), x2 (t),..., xn (t)), for known values of u (t) = (u1 (t), u2 (t),..., um (t)). A situation arises when it is necessary to solve a system of interrelated equations, but this system is not defined. In this case, it is possible to use a sequential chain of algorithms to find the values of the components of the vector of output variables x(t) from the known input u(t). The task of controlling a discrete-continuous process is considered under conditions of nonparametric uncertainty, that is, when the object in question is not described up to the parameter vector α. In this case, it is advisable to use a chain of control algorithms to search for the corresponding control action u(t) at each step. If the dimension of the input vector u (t) exceeds the dimension of the output vector x(t), then some of the components of the input variables u (t) can be interpreted as uncontrolled, but controlled. This often corresponds to actual technological processes. We have carried out numerous computational experiments on the identification and control of T-processes, which have shown a fairly high efficiency. The article presents some fragments of numerical studies. In this case, options were considered with different dimensionalities of objects, the level of interference, the volume of training samples, and others. © 2020 Tomsk State University. All rights reserved.
Журнал: VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-UPRAVLENIE VYCHISLITELNAJA TEHNIKA I INFORMATIKA-TOMSK STATE UNIVERSITY JOURNAL OF CONTROL AND COMPUTER SCIENCE
Выпуск журнала: Is. 53
Номера страниц: 72-81
ISSN журнала: 19988605
Место издания: TOMSK
Издатель: TOMSK STATE UNIV