Optimal control problem for stochastic evolution equations in Hilbert spaces

作者：Zhou Jianjun; Liu Bin^*

来源：International Journal of Control, 2010, 83(9): 1771-1784.

DOI：10.1080/00207179.2010.495161

• optimal control
• backward stochastic differential equations
• stochastic evolution equations
• quadratic growth

In this article, we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value. As an application, an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results.

• 出版日期2010
• 单位华中科技大学