一类具有非局部积分条件的2b -抛物型方程的最优控制问题

I. Pukalskyy, I. Luste
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引用次数: 0

摘要

研究了系统的最优控制选择问题,该问题被描述为一个具有时间上的积分条件的抛物线问题,该问题具有有限的内部控制和启动控制。质量标准将由体积积分的总和给出。利用2b-抛物型方程Cauchy问题的基本解,建立了在时间变量上具有积分条件的2b-抛物型方程解的存在性、统一性和积分表示。给出了具有积分条件的2b-抛物型方程在时间上的非局部问题解的估计及其在Hölder空间上的导数。所得结果已用于最优控制问题的研究。利用泰勒公式和非局部问题解的积分表示,得到了以时间变量为积分条件的2b-抛物型方程问题所描述的系统存在最优控制的充分必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
OPTIMAL CONTROL PROBLEM FOR A 2B-PARABOLIC EQUATION WITH AN INTEGRAL NON-LOCAL CONDITION
The problem of choosing the optimal control of the system, which is described by a parabolic problem with an integral condition over the time and limited internal and starting control, is investigated. The quality criterion will be given by the sum of volume integrals. Using the fundamental solution of the Cauchy problem for the 2b-parabolic equation, the existence, unity and integral representation of the solutions of the problem for the 2b-parabolic equation with the integral condition on the time variable were established. Estimates of the solution of the nonlocal problem for the 2b-parabolic equation with integral condition in time and its derivatives in Hölder spaces are found. The obtained result was used in the study of the problem of optimal control. With the help of the Taylor formula and the integral representation of the solutions of the nonlocal problem, the necessary and sufficient conditions for the existence of the optimal control of the system described by the problem for the 2b-parabolic equation with the integral condition for the time variable were found.
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