On regularization of the Lagrange principle in the optimization problems for linear distributed Volterra type systems with operator constraints

IF 0.3 Q4 MATHEMATICS
V. Sumin, M. I. Sumin
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引用次数: 0

Abstract

Regularization of the classical optimality conditions - the Lagrange principle and the Pontryagin maximum principle - in a convex optimal control problem subject to functional equality and inequality constraints is considered. The controlled system is described by a linear functional-operator equation of second kind of the general form in the space $L_2^m$. The main operator on the right-hand side of the equation is assumed to be quasi-nilpotent. The objective functional to be minimized is strongly convex. The derivation of the regularized classical optimality conditions is based on the use of the dual regularization method. The main purpose of the regularized Lagrange principle and regularized Pontryagin maximum principle is to stably generate minimizing approximate solutions in the sense of J. Warga. As an application of the results obtained for the general linear functional-operator equation of second kind, two examples of concrete optimal control problems related to a system of delay equations and to an integro-differential transport equation are discussed.
带算子约束的线性分布Volterra型系统优化问题中拉格朗日原理的正则化
研究了一类具有函数等式和不等式约束的凸最优控制问题中经典最优性条件拉格朗日原理和庞特里亚金极大值原理的正则化问题。被控系统用空间$L_2^m$中一般形式的第二类线性泛函算子方程来描述。假设方程右边的主算子是拟幂零的。要最小化的目标泛函是强凸的。正则化经典最优性条件的推导基于对偶正则化方法的使用。正则化拉格朗日原理和正则化庞特里亚金极大值原理的主要目的是稳定地生成J. Warga意义上的最小化近似解。作为对第二类一般线性泛函算子方程所得结果的应用,讨论了与时滞方程组和积分-微分输运方程有关的两个具体最优控制问题。
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