scholarly journals Point control of a differential-difference system with distributed parameters on the graph

2021 ◽  
Vol 17 (3) ◽  
pp. 277-286
Author(s):  
Vyacheslav V. Provotorov ◽  
◽  
Sergey M. Sergeev ◽  
Hoang Van Nguyen ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Universal Method ◽  
Difference System ◽  
Optimal Point ◽  
Conjugate System ◽  
Distributed Parameters ◽  
Conjugate State ◽  
Point Control ◽  
Multi Phase

The article considers the problem of point control of the differential-difference equation with distributed parameters on the graph in the class of summable functions. The differential- difference system is closely related to the evolutionary differential system and moreover the properties of the differential system are preserved. This connection is established by the universal method of semi-discretization in a time variable for a differential system, which provides an effective tool in order to find conditions for unique solvability and continuity on the initial data for the differential-difference system. For this differential-difference system, a special case of the optimal control problem is studied: the problem of point control action on the controlled differential-difference system is considered by the control, concentrated at all internal nodes of the graph. At the same time, the restrictive set of permissible controls is set by the means of conditions depending on the nature of the applied tasks. In this case, the controls are concentrated at the end points of the edges adjacent to each inner node of the graph. This is a characteristic feature of the study presented, quite often used in practice when building a mechanism for managing the processes of transportation of different kinds of masses over network media. The study essentially uses the conjugate state of the system and the conjugate system for a differential-difference system — obtained ratios that determine optimal point control. The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on the graph, which have interesting analogies with multi-phase problems of multidimensional hydrodynamics.

scholarly journals Optimal control of pulse compensators of oscillatory phenomena in a network oil and gas pipeline system

2021 ◽  
Vol 2094 (5) ◽  
pp. 052024
Author(s):  
S A Tkachova ◽  
A S Maltsev ◽  
A A Fedotov ◽  
A S Gunkina ◽  
O Ja Kravets
Keyword(s):  
Optimal Control ◽  
Mathematical Description ◽  
Continuous Medium ◽  
Oil And Gas ◽  
Hyperbolic Equations ◽  
Oscillatory Process ◽  
Pipeline System ◽  
Difference System ◽  
Point Control ◽  
Network Carrier

Abstract Within the framework of oil and gas engineering, the problem of optimal control of pulse compensators that counteract harmful oscillatory phenomena in a continuous medium during transportation via network gas-hydraulic carriers is considered. Powerful compressor units that create high pressure in the carrier of a continuous medium, to a large extent contribute to the formation of undesirable oscillatory phenomena (pulsations) that occur at the output of these compressors. These ripples are transmitted to the network carrier environment, which significantly reduces the efficiency of compressor units and even causes accidents in the networks of gas and hydraulic carriers. The latter means that the software engineering of the oil and gas industry should include research in the direction of improving the reliability of operation of compressor units and gas-hydraulic carriers. In the presented study, the mathematical description of the oscillatory process of a continuous medium is carried out by formalisms of a differential-difference system of hyperbolic equations with distributed parameters on a graph. At the same time, the mathematical model contains a fairly accurate mathematical description of controlled pulse compensators. The problem of controlling pulse compensators of an oscillatory process is considered as the problem of a point control action on a controlled differential-difference system at the places where continuous medium vibration dampers are connected to a network carrier. This is a characteristic feature of the presented study, which is quite often used in practice when engineering the processes of transporting various kinds of continuous media through network oil and gas carriers. The study essentially uses the conjugate state and the conjugate system for a differential-difference system - the relations determining the optimal point control are obtained. The results of the work are applicable in the framework of oil and gas engineering to the study of issues of stabilization and parametric optimization.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

scholarly journals Two-channel time-optimal control of nonstationary heat conductive process with account for response time of boundary control actions

2021 ◽  
Vol 29 (2) ◽  
pp. 47-60
Author(s):  
Natalya A. Il’ina
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Optimal Time ◽  
Time Control ◽  
Distributed Parameters ◽  
Control Actions ◽  
Optimal Controllers ◽  
Time Optimal

The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

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