IJPAM: Volume 62, No. 1 (2010)

SUCCESSIVE APPROXIMATIONS FOR OPTIMAL CONTROL
IN SOME STOCHASTIC SYSTEMS WITH
SMALL PARAMETER

Alexander Spivak
Department of Applied Mathematics
Holon Institute of Technology
P.O. Box 305, Holon, 58102, ISRAEL
e-mail: spivak@hit.ac.il


Abstract.Optimal control synthesis is constructed for systems with the help of perturbations in the form of small nonlinear terms of order $\epsilon$, and also of the form of standard Gaussian white noise. The minimized functional differs from the quadratic one by some nonlinear term. When $\epsilon=0$, the optimal control synthesis is found in an exact analytic form. Successive approximations to the optimal control are constructed with the help of the perturbation method.

Received: April 28, 2010

AMS Subject Classification: 49J15, 58E25, 49M30

Key Words and Phrases: optimal control, perturbation theory, successive approximations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 1