TY - JOUR
T1 - Towards the optimal control of Markov chains with constraints
AU - Miller, Boris
AU - Miller, Gregory
AU - Siemenikhin, Konstantin
PY - 2010
Y1 - 2010
N2 - An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov
chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution
existence is proved under a natural assumption that the set of admissible controls is non-empty. The
stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution
satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis
of this result an approach to the numerical solution is proposed and its implementation is illustrated by
examples.
AB - An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov
chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution
existence is proved under a natural assumption that the set of admissible controls is non-empty. The
stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution
satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis
of this result an approach to the numerical solution is proposed and its implementation is illustrated by
examples.
UR - http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V21-50DNKXH-1&_user=542840&_coverDate=09%2F30%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin
U2 - 10.1016/j.automatica.2010.06.003
DO - 10.1016/j.automatica.2010.06.003
M3 - Article
SN - 0005-1098
VL - 46
SP - 1495
EP - 1502
JO - Automatica
JF - Automatica
IS - 9
ER -