arXiv 1002.30672010-02quant-phmath.OC

Numerical Solution of the Dynamic Programming Equation for the Optimal Control of Quantum Spin Systems

Srinivas Sridharan, Matthew R. James

备注：: 11 pages, 5 figures
DOI：: 10.1016/j.sysconle.2011.05.010

英文摘要：

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined on a Lie group. We employ recent extensions of the theory of viscosity solutions from Euclidean space to Riemannian manifolds to interpret possibly non-differentiable solutions to this equation. Results from differential topology on the triangulation of manifolds are then used to develop a finite difference approximation method, which is shown to converge using viscosity solution techniques. An example is provided to illustrate the method.

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