Title

MARKOV DECISION PROCESSES ON BOREL SPACES
WITH RANDOM HORIZON AND
NONZERO TERMINAL COST

Authors

Ilhuicatzi-Roldán Rocio, Flores-Hernández Rosa M.
Facultad de Ciencias Básicas, Ingenierıa y Tecnologıa
Universidad Autónoma de Tlaxcala
Av. Ángel Solana s/n, Apizaco, 90300, MÉXICO
Facultad de Ciencias Básicas, Ingenierıa y Tecnologıa
Universidad Autónoma de Tlaxcala
Calz. Apizaquito s/n, Apizaco, 90300, MÉXICO

Abstract

In this paper, an optimal control problem with the expected total cost as performance criterion is considered. In this case, a random horizon and a nonzero terminal cost in the performance criterion is supposed. The terminal cost depends on the state of the system at the random occurrence time of termination of the process. Then, under the assumption that the random horizon is independent of the stochastic control process and its probability distribution has a finite support, the dynamic programming equation is obtained, which solves the problem proposed. Also, two examples are included, one is a linear quadratic control problem and other is an inventory control problem, both with a random horizon and a nonzero terminal cost.

History

Received: June 21, 2017
Revised: March 21, 2018
Published: July 4, 2018

AMS Classification, Key Words

AMS Subject Classification: 93E20, 90C40, 90C39
Key Words and Phrases: Markov decision process, total cost, random horizon, nonzero terminal cost

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Bibliography

1

D.P. Bertsekas, Dynamic Programming: Deterministic and Stochastic Models, Prentice-Hall, USA, 1987.

2

D.P. Bertsekas, S.E. Shreve, Stochastic Optimal Control: The Discrete Time Case, Academic Press, Massachusetts, 1978.

3

H. Cruz-Suárez, R. Ilhuicatzi-Roldán, R. Montes-de-Oca, Markov decision processes on Borel spaces with total cost and random horizon, Journal of Optimization Theory and Applications, 162 (2013), 329-346.

How to Cite?

DOI: 10.12732/ijpam.v119i2.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 2
Pages: 343 - 356

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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