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

Per Rutquist ; Torsten Wik (Institutionen för signaler och system, Reglerteknik) ; Claes Breitholtz (Institutionen för signaler och system, Reglerteknik)
Proceedings of the 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15-17 December 2014 (0743-1546). p. 1840-1845. (2014)
[Konferensbidrag, refereegranskat]

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.



Denna post skapades 2015-03-29. Senast ändrad 2015-07-07.
CPL Pubid: 214484

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Reglerteknik

Ämnesområden

Optimeringslära, systemteori
Reglerteknik

Chalmers infrastruktur