Adaptive control of diffusion processes with a discounted reward criterion

B. A. Escobedo-Trujillo; O. Hernández-Lerma; F. A. Alaffita-Hernández

doi:10.4064/am2421-10-2020

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Adaptive control of diffusion processes with a discounted reward criterion

B. A. Escobedo-Trujillo ¹ ; O. Hernández-Lerma ² ; F. A. Alaffita-Hernández ³

¹ Facultad de Ingeniería Universidad Veracruzana Av. Universidad km 7.5 C.P. 96535, Coatzacoalcos, Veracruz, México <a href="https://orcid.org/0000-0002-8937-3019">ORCID: 0000-0002-8937-3019</a>
² Departamento de Matemáticas CINVESTAV-IPN A. Postal 14-740 <a href="https://orcid.org/0000-0003-3308-5218">ORCID: 0000-0003-3308-5218</a>
³ Centro de Investigación en Recursos Energéticos y Sustentables Universidad Veracruzana Av. Universidad km 7.5 C.P. 96535, Coatzacoalcos, Veracruz, México <a href="https://orcid.org/0000-0002-7971-6356">ORCID: 0000-0002-7971-6356</a>

Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 225-253.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/am2421-10-2020

Keywords: optimal control problem dealing paper determine control policies maximize discounted reward criterion dynamic system evolves stochastic differential equation sde instantaneous reward function sde drift coefficient may depend unknown parameter conditions ensuring existence asymptotically optimal policy using so called principle estimation control illustrate results several examples

Affiliations des auteurs :

B. A. Escobedo-Trujillo ¹ ; O. Hernández-Lerma ² ; F. A. Alaffita-Hernández ³

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B. A. Escobedo-Trujillo; O. Hernández-Lerma; F. A. Alaffita-Hernández. Adaptive control of diffusion processes with a discounted reward criterion. Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 225-253. doi : 10.4064/am2421-10-2020. http://geodesic.mathdoc.fr/articles/10.4064/am2421-10-2020/

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