Adaptive control of diffusion processes with a discounted reward criterion

Volume 47 / 2020

B. A. Escobedo-Trujillo, O. Hernández-Lerma, F. A. Alaffita-Hernández Applicationes Mathematicae 47 (2020), 225-253 MSC: 93E10, 93E20, 93E24, 60J60. DOI: 10.4064/am2421-10-2020 Published online: 9 December 2020

Abstract

The optimal control problem we are dealing with in this paper is to determine control policies that maximize a discounted reward criterion when the dynamic system evolves as a stochastic differential equation (SDE). Both the instantaneous reward function and the SDE’s drift coefficient may depend on an unknown parameter. We give conditions ensuring the existence of an asymptotically optimal policy using the so-called Principle of Estimation and Control. We illustrate our results with several examples.

Authors

  • B. A. Escobedo-TrujilloFacultad de Ingeniería
    Universidad Veracruzana
    Av. Universidad km 7.5
    C.P. 96535, Coatzacoalcos, Veracruz, México
    ORCID: 0000-0002-8937-3019
    e-mail
  • O. Hernández-LermaDepartamento de Matemáticas
    CINVESTAV-IPN
    A. Postal 14-740
    ORCID: 0000-0003-3308-5218
    e-mail
  • F. A. Alaffita-HernándezCentro de Investigación en Recursos Energéticos y Sustentables
    Universidad Veracruzana
    Av. Universidad km 7.5
    C.P. 96535, Coatzacoalcos, Veracruz, México
    ORCID: 0000-0002-7971-6356
    e-mail

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