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**Harvard**

Rutquist, P., Wik, T. och Breitholtz, C. (2014) *Solving the Hamilton-Jacobi-Bellman equation for a stochastic system with state constraints*.

** BibTeX **

@conference{

Rutquist2014,

author={Rutquist, Per and Wik, Torsten and Breitholtz, Claes},

title={Solving the Hamilton-Jacobi-Bellman equation for a stochastic system with state constraints},

booktitle={Proceedings of the 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15-17 December 2014},

pages={1840-1845},

abstract={We present a method for finding a stationary solution to the Hamilton-Jacobi-Bellman (HJB) equation for a stochastic system with state constraints. A variable transformation is introduced which turns the HJB equation into a combination of an eigenvalue problem, a set of partial differential equations (PDEs), and a point-wise equation. As a result the difficult infinite boundary conditions of the original
HJB becomes homogeneous. To illustrate, we numerically solve for the optimal control of a Linear Quadratic Gaussian (LQG) system with state constraints. A reasonably accurate solution is obtained even with a very small number of collocation points (three in each dimension), which suggests that the method could be used on high order systems, mitigating the curse of dimensionality. Source code for the example is available online.},

year={2014},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 214484

A1 Rutquist, Per

A1 Wik, Torsten

A1 Breitholtz, Claes

T1 Solving the Hamilton-Jacobi-Bellman equation for a stochastic system with state constraints

YR 2014

T2 Proceedings of the 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15-17 December 2014

SP 1840

OP 1845

AB We present a method for finding a stationary solution to the Hamilton-Jacobi-Bellman (HJB) equation for a stochastic system with state constraints. A variable transformation is introduced which turns the HJB equation into a combination of an eigenvalue problem, a set of partial differential equations (PDEs), and a point-wise equation. As a result the difficult infinite boundary conditions of the original
HJB becomes homogeneous. To illustrate, we numerically solve for the optimal control of a Linear Quadratic Gaussian (LQG) system with state constraints. A reasonably accurate solution is obtained even with a very small number of collocation points (three in each dimension), which suggests that the method could be used on high order systems, mitigating the curse of dimensionality. Source code for the example is available online.

LA eng

DO 10.1109/CDC.2014.7039666

LK http://dx.doi.org/10.1109/CDC.2014.7039666

OL 30