Linear theory for control of nonlinear stochastic systems.
We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of nonlinear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exists a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by a Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.
Kappen
Hilbert J
HJ
Department of Medical Physics & Biophysics, Radboud University, Geert Grooteplein 21 6525 EZ Nijmegen, The Netherlands. B.Kappen@science.ru.nl