CUED Publications database

Optimal control with stochastic PDE constraints and uncertain controls

Rosseel, E and Wells, GN (2012) Optimal control with stochastic PDE constraints and uncertain controls. Computer Methods in Applied Mechanics and Engineering, 213-21. pp. 152-167. ISSN 0045-7825

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Abstract

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Item Type: Article
Uncontrolled Keywords: Optimal control Stochastic finite element method Stochastic inverse problems Stochastic partial differential equations Uncertainty
Subjects: UNSPECIFIED
Divisions: Div C > Applied Mechanics
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:29
Last Modified: 11 Dec 2014 19:02
DOI: 10.1016/j.cma.2011.11.026