Banisch, Ralf and Hartmann, C. (2016) A sparse Markov chain approximation of LQtype stochastic control problems. Math. Control Relat. F., 6 (3). pp. 363389. ISSN 10648275

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Abstract
We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linearquadratic in the controls, but possibly nonlinear in the state variables, and the discretization is based on the fact that problems of this kind admit a dual formulation in terms of linear boundary value problems. We show that the discretized linear problem is dual to a Markov decision problem, prove an $L^{2}$ error bound for the general scheme and discuss the sparse discretization using a basis of socalled committor functions as a special case; the latter is particularly suited when the dynamics are metastable, e.g., when controlling biomolecular systems. We illustrate the method with several numerical examples, one being the optimal control of Alanine dipeptide to its helical conformation.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  1507 
Deposited By:  Carsten Hartmann 
Deposited On:  17 Feb 2015 23:30 
Last Modified:  13 Dec 2017 14:33 
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