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The problem of control of the process described by the nonlinear differential equation with partial derivatives of the first order, with conditions at t 0 and in a sequence n of points x1 < x2 ... < xn is solved. The criterion of quality of control is the integrated quadratic functional, which depends on a final state of system and set n of controlling parameters. The method of increment of functional is applied to reception of conditions of optimality, and the method of additional argument (MAA) is applied for the decision of the nonlinear equations with partial derivatives.
In this study, a problem related with management functions for boundry and Cauchy problems in linear integro-differential systems having Fredholm Integrals is taken in hand and the solution is done with the help of using minimum Power.
For the singularly perturbed parabolic problem, a regularized asymptotics of the solution of the problem of optimal control was constructed. The solution asymptotics involves parabolic boundary-layer functions obeying a special function called the “complementary probability integral.
Cтроится регуляризованная асимптотика решения задачи оптимальногоуправления для сингулярно возмущенной параболической задачи. Асимптотика решения такой задачи содержит параболические погранслойные функции, описываемые специальной функцией, называемой “дополнительным интегралом вероятности”.
The problem of minimum-energy control in the integro-differential linear systems with Fredholm integral was solved using the N.N. Krasovskii method of the problem of moments. An explicit solution of the boundary problem for the integro-differential equation was established using the K.A. Kasymov method.
Методом проблемы моментов, разработанным Н. Н. Красовским [1], решается задача управления с минимальной энергией в линейных интегро-дифференциальных системах с интегралом типа Фредгольма. Явный вид решения краевой задачи для интегро-дифференциального уравнения находится методом, предложенным К. А. Касымовым [2]
The problem of minimization of atmosphere pollution by fractions of harmful admixtures is studied. It is supposed that a controlled object is described by non-stationary integral–differential transfer equation with special boundary conditions and control parameters, which are included in the right part of equation as delta-functions. Minimized integral quadratic functional characterizes energy expenditure for control and depends on the average squared deflection of fraction concentration from the desired final state. Optimal conditions are obtained with the help of Pontryagin’s maximum princip ...Более