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The authors considered the problem of optimal control of loading points and the corresponding reaction functions described by a loaded parabolic equation. They obtained optimality conditions for control actions. The authors used the objective functional gradient formulas contained in these conditions in the algorithm for numerically solving the problem of controlling the movement of loading points and corresponding reaction functions based on first-order optimization methods. The paper provides the results of numerical experiments. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the optimal control problem for a linear system of ordinary differential equations with linear boundary conditions. The boundary conditions involve the values of the phase variable both at separate intermediate points and their integral values over individual intervals of the independent variable. In the problem, we determine the controls involved in the differential equations and the values of the right-hand sides of multipoint and integral boundary conditions. The necessary conditions for the existence and uniqueness of the solution to the boundary value problem, the convexity of the objective functional and the necessary optimality conditions for the optimizable parameters are obtained. The conditions contain constructive formulas of the gradient components of the functional. The numerical solution of an illustrative problem is considered. [ABSTRACT FROM AUTHOR]

In this paper, a heating process control law with steam supply is designed for a fluid in a heat exchanger. The process is described by a linear hyperbolic equation of the first order with a nonlocal boundary condition with a time-delayed argument. The temperature of the supplied steam is found as a linear dependence on fluid temperature values at measurement points in the heat exchanger. Explicit formulas are obtained for the gradient of the objective functional of the control problem in the space of the feedback coefficients (parameters) of this dependence. A numerical scheme is developed for determining the feedback parameters based on these formulas. Finally, an algorithm is proposed for determining the rational (optimal) number of measurement points. [ABSTRACT FROM AUTHOR]

Using the process of heating a rod in a furnace as an example, we study the feedback control synthesis problem for plants with distributed parameters. To form the control values, it is proposed to use their linear dependence on the state values at the points of measurement, both at the current and at the preceding moments of time. The unknown coefficients involved in this dependence of the control on the measured state values are the feedback parameters. They are determined by minimizing the objective functional using first-order numerical optimization methods. To this end, formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

The problem of optimizing the right-hand sides of linear nonlocal multipoint conditions for a linear system of differential equations is considered. Necessary optimality conditions of the first order are obtained, which allow the use of efficient first-order methods for the numerical solution of the problem under consideration. Solutions of test problems are presented and analyzed. [ABSTRACT FROM AUTHOR]

We study an optimal control problem described by a system of linear ordinary differential equations with boundary conditions containing point and integral values of the state variable. The controls occurring in the differential equations and the values of the right-hand sides of the nonlocal boundary conditions are determined in this problem. Necessary conditions for the existence and uniqueness of a solution of the boundary value problem and for the convexity of the objective functional, as well as necessary conditions for the optimality of the parameters to be optimized in the control problem, are studied. The formulas obtained for the gradient of the objective functional of the problem are used in the numerical solution of an illustrative problem. The results of numerical experiments are provided. [ABSTRACT FROM AUTHOR]

The paper studies the solution to an optimal control problem for the process of circulating coolant heating in the heat supply system. The amount of heat supplied for coolant heating in the steam furnace is defined by a linear dependence on the temperature measured in the sensing points. The problem involves optimization of linear feedback parameters, locations and number of sensing points. Formulas have been obtained for gradient of the functional being optimized, which are used in first-order optimization methods. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

An approach to the numerical solution of an optimal control problem described by systems of ordinary differential equations with point loading is proposed. The problem involves nonlocal conditions in which the values of the phase state at certain points and its integral values on various preset intervals are contained in coupled form. For the cost functional gradient of the problem, formulas are derived, which are used to solve the problem by applying numerical optimization methods of the first order. Results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

The problem of optimizing the number and locations of state observation points in the feedback control of heating a rod in a furnace is considered. The weighting coefficients determining the importance of each observation point in the current linear control function are also optimized. The synthesis of control functions is reduced to the problem of optimizing parameters for a pointwise loaded parabolic equation, which is solved by applying first-order optimization methods. [ABSTRACT FROM AUTHOR]