SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1628-1655, January 2021.
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform.

中文翻译：

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状态约束控制仿射抛物线问题II：二阶充分的最优性条件

SIAM控制与优化杂志，第59卷，第2期，第1628-1655页，2021
年1月。在本文中，我们考虑由具有双线性控制状态项的半线性热方程控制并受控制和状态约束的最优控制问题。状态约束是积分类型的，积分是相对于空间变量的。该控件是多维的。成本函数为跟踪类型，在控制变量中包含线性项。我们依靠Goh变换得出二阶充分条件。