进化系统优化控制中的二阶充分条件

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-04-27 DOI:10.1007/s00028-024-00968-5

H. Frankowska, E. M. Marchini, M. Mazzola

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引用次数: 0

摘要

本文涉及控制约束和终点约束下一类无限维最优控制问题的二阶最优充分条件。我们提出的问题的显著特点是使用了变分分析技术。我们的方法基于对控制的适当分解，使用二阶切线，并且是在函数约束的情况下开发的。我们还提出了在控制点约束情况下对工具的调整。我们提供了涉及 PDE 的具体最优控制问题的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Second-order sufficient conditions in optimal control of evolution systems

This paper concerns second-order sufficient conditions of optimality for a class of infinite dimensional optimal control problems under control constraints and end-point constraints. The distinctive feature of our formulation is the use of variational analysis techniques. Our approach is based on a suitable decomposition of controls, using second-order tangents, and it is developed in the case of functional constraints. An adaptation of the tools in the case of pointwise constraints on the controls is proposed too. We provide applications to concrete optimal control problems involving PDEs.

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators