半线性抛物型方程最优控制的值函数

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-09-25 DOI:10.1016/j.nonrwa.2025.104508

Eduardo Casas , Karl Kunisch , Fredi Tröltzsch

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引用次数: 0

摘要

研究了一类具有半线性抛物型方程的无限视界跟踪型最优控制问题的值函数。考虑到最优控制问题可能存在的非凸性，考虑了值函数的局部形式。在满足二阶充分最优条件的条件下，证明了该方法在标称局部最优控制的邻域内初始数据的可微性。基于值函数的可微性，导出了Hamilton-Jacobi-Bellman方程。

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On the value function for optimal control of semilinear parabolic equations

The value function for an infinite horizon tracking type optimal control problem with semilinear parabolic equation is investigated. In view of a possible nonconvexity of the optimal control problem, a local version of the value function is considered. Its differentiability is proved for initial data in a neighborhood around the nominal initial value, provided a second order sufficient optimality condition is fulfilled for the nominal locally optimal control. Based on the differentiability of the value function, a Hamilton-Jacobi-Bellman equation is derived.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.