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1
Content available remote A time-changed stochastic control problem and its maximum principle
Nane Erkan, Ni Yinan
Probability and Mathematical Statistics
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2021
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Vol. 41, Fasc. 2
193--215
EN
This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a Lévy noise time-changed by an inverse subordinator. We establish a maximum principle for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differ- ential equation involved in the stochastic control problem. Some examples are provided for illustration.
2
Content available Minimizing the time spent in an interval by a Wiener process with uniform jumps
Lefebvre Mario
Control and Cybernetics
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2019
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Vol. 48, No. 3
407--415
EN
Let Xu(t) be a controlled Wiener process with jumps that are uniformly distributed over the interval [−c, c]. The aim is to minimize the time spent by Xu(t) in the interval [a, b]. The integro- differential equation, satisfied by the value function, is transformed into an ordinary differential equation and is solved explicitly for a particular case. The approximate solution obtained is precise when c is small.
3
Content available Information and analytical technology for control and operation management of gas transportation systems operation modes
Tevyashev Andriy, Iievlieva Svitlana
Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy
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2018
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nr 21
69--84
EN
The purpose of the study is to develop new information and analytical technologies and tools for optimal stochastic control of the technological processes of production, preparation, transportation and distribution of energy resources in the gas transportation systems of Ukraine. The achievement of this goal will enable us to implement a unified, well-balanced approach to the modernization and rational development the gas transportation systems of Ukraine based on achieving maximum indicators in resource saving and environmentally friendly technologies in energy, which is currently extremely relevant.
PL
Celem badań jest opracowanie nowych technologii narzędzi informacyjnych i analitycznych dla optymalnego stochastycznego sterowania procesami technologicznymi produkcji, przygotowania, transportu i dystrybucji surowców energetycznych w systemach transportu gazu na Ukrainie.
4
Content available About one class of the problems of optimal stochastic control of hybrid dynamical systems
Tevyashev A., Matviyenko O.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2016
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Vol. 5, No 4
3--10
EN
A new class of the problems of optimal stochastic control of hybrid dynamical systems different from well-known ones by the introduction of additional extreme and probabilistic constraints on the phase variables is studied in the present work. The mathematical formulation and approximate method of solution of the examined class of the problems are presented in this work. The effectiveness of the use of this class of the problems is illustrated on the example of one of the largest water main of Ukraine.
5
Content available Optimal stochastic control of the modes of operation of the sewage pumping station
Tevyashev A., Nikitenko G., Matviyenko O.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2015
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Vol. 4, No 3
47--55
EN
In this work we propose a new mathematical model and method of optimal stochastic control of the modes of operation of the sewage pumping station for three-band tariff for the electricity, the implementation of which provides a significant reduction of financial expenses of the electricity for pumping waste water. The proposed model and method Take into account the stochastic properties of the object of control and environment most adequately. The mathematical formulation of the problem of optimal stochastic control with extreme and probabilistic constraints on the phase variables and efficient algorithm to solve it is presented. The proposed method of optimal stochastic control provides minimum of the mathematical expectation of the volumes of pumped waste water at the time interval with a high electricity tariff and maximum of the mathematical expectation of the volumes of pumped waste water at the time interval with a minimal tariff when all technological limitations are accomplished.
6
Content available About one problem of optimal stochastic control of the modes of operation of water mains
Tevyashev A., Matviyenko O.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2015
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Vol. 4, No 3
3--12
EN
The problem of increasing of the efficiency of operation of the water mains in modern conditions while the transition to a three-tier tariff for the electricity is examined in the present work. An effective method for solving this problem, based on the use of specific features of the water mains as stochastic objects operating in the stochastic environment is offered. The mathematical formulation of the problems of optimal stochastic control of the modes of operation of the water main with probabilistic constraints on the phase variables is presented. A new strategy for the optimal stochastic control of the modes of operation of the water main, the use of which has allowed to develop an effective method for solving the examined problem is proposed in the present work. It is shown that the transition from the classical deterministic problems of control of the modes of operation of the water mains to stochastic ones, provides a significant (up 9%) decrease of financial expenses for the electricity.
7
Content available remote Optimal control for a nonstationary linear system with a quadratic cost functional
Czornik Adam
Matematyka Stosowana : matematyka dla społeczeństwa
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1997
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Nr 40
3--11
EN
This paper is about optimal control of infinite-horizon nonstationary stochastic linear processes with a quadratic cost criterion. The synthesis problem of optimal control is solved under the assumptions that the criterion is an average expected cost and that the process' matrices possess limits for the time approaching infinity. Furthermore, the limit matrices are such that the "limit" process is both observable and controllable. The paper documents existence of an optimal feedback control policy. The policy is such that the gain matrix is a (scaled) solution to a Riccati stationary matrix equation. The equation is stationary in that its coefficients are the limits of the process' non-stationary matrices.
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