Optimal Control for Stochastic Delay Evolution Equations

Journal Article · Mon Aug 15 04:00:00 EDT 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-015-9308-2· OSTI ID:22617267

Meng, Qingxin ^[1]; Shen, Yang ^[2]

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1. Huzhou University, Department of Mathematical Sciences (China)
2. York University, Department of Mathematics and Statistics (Canada)

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

• OSTI ID: 22617267
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 74; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CAUCHY PROBLEM
DIRICHLET PROBLEM
EVOLUTION
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
PARTIAL DIFFERENTIAL EQUATIONS
RANDOMNESS
STOCHASTIC PROCESSES