IJPAM: Volume 55, No. 2 (2009)

OPTIMAL CONTROL PROBLEMS WITH
RANDOM FINAL TIME

Mario Lefebvre
Department of Mathematics and Industrial Engineering
École Polytechnique
C.P. 6079, Succursale Centre-Ville
Montreal, Quebec, H3C 3A7, CANADA
e-mail: mlefebvre@polymtl.ca


Abstract.Problems involving controlled one-dimensional diffusion processes $X(t)$ over a random time interval are considered. The infinitesimal variance of the processes depends on the control variable. The processes are controlled until they leave the interval $(d_1,d_2)$. The cost criterion whose expected value we want to minimize is such that, in addition to the quadratic control costs, a final cost is incurred if $X[\tau(x)]=d_2$, where $\tau(x)$ is the random final time. Exact and explicit solutions are obtained in special cases both for the optimal control and for the value function. A related game theory problem is also presented.

Received: February 11, 2007

AMS Subject Classification: 93E20, 49N70

Key Words and Phrases: LQG homing, Brownian motion, hitting time, game theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2