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Solving the Hamilton-Jacobi-Bellman Equation for a Stochastic System with State Constraints

Per Rutquist (Institutionen för signaler och system, Reglerteknik) ; Torsten Wik (Institutionen för signaler och system, Reglerteknik) ; Claes Breitholtz (Institutionen för signaler och system, Reglerteknik)
Göteborg : Chalmers University of Technology, 2014. - 13 s.
[Rapport]

We present a method for solving 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 a linear eigenvalue problem, a set of partial differential equations (PDE:s), and a point-wise equation. For a fixed solution to the eigenvalue problem, the PDE:s are linear and the point-wise equation is quadratic, indicating that the problem can be solved efficiently using an iterative scheme. As an example, 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.


Report has been submitted to the 53rd IEEE Conference on Decision and Control, with identical content but a different layout



Denna post skapades 2014-03-21. Senast ändrad 2014-04-04.
CPL Pubid: 195410

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Reglerteknik

Ämnesområden

Reglerteknik

Chalmers infrastruktur

Ingår i serie

R - Department of Signals and Systems, Chalmers University of Technology R007/2014