An efficient sampling method is proposed to solve the stochastic optimal control problem in the context of data assimilation for the estimation of a random parameter. It is based on Bayesian inference and the Markov Chain Monte Carlo technique, which exploits the relation between the inverse Hessian of the cost function and the error covariance matrix to accelerate convergence of the sampling method. The efficiency and accuracy of the method is demonstrated in the case of the optimal control problem governed by the nonlinear Burgers equation with a viscosity parameter that is a random field.
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Optimal Control and Stochastic Parameter Estimation
11. Department of Mathematics, Florida A&M University, Tallahassee, Florida 32307, USA
22. School of Computational Science, Florida State University, Tallahassee, Florida 32306-4120, USA
∗Permanent address: Laboratoire de Modélisation et Calcul, Projet IDOPT, Université Joseph Fourier, 38041 Grenoble cedex 9, France
Citation Information: Monte Carlo Methods and Applications mcma. Volume 12, Issue 5, Pages 461–476, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/156939606779329062,
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Key Words: Monte Carlo method,; covariance matrix,; Hessian matrix,; Bayesian inference,; Burgers equation.
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