Robust Statistic Estimation of Constrained Optimal Control Problems of Pollution Accumulation (Part I)

Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos (), Carmen Geraldi Higuera-Chan and Francisco Alejandro Alaffita-Hernández
Additional contact information
Beatris Adriana Escobedo-Trujillo: Facultad de Ingeniería, Universidad Veracruzana, Coatzacoalcos 96535, Mexico
José Daniel López-Barrientos: Facultad de Ciencias Actuariales, Universidad Anáhuac México, Naucalpan de Juárez 52786, Mexico
Carmen Geraldi Higuera-Chan: Departamento de Matemáticas, Universidad de Sonora, Hermosillo 83000, Mexico
Francisco Alejandro Alaffita-Hernández: Centro de Investigación en Recursos Energéticos y Sustentables, Universidad Veracruzana, Coatzacoalcos 96535, Mexico

Mathematics, 2023, vol. 11, issue 4, 1-19

Abstract: In this paper, we study a constrained optimal control on pollution accumulation where the dynamic system was governed by a diffusion process that depends on unknown parameters, which need to be estimated. As the true values are unknown, we intended to determine (adaptive) policies that maximize a discounted reward criterion with constraints, that is, we used Lagrange multipliers to find optimal (adaptive) policies for the unconstrained version of the optimal control problem. In the present context, the dynamic system evolves as a diffusion process, and the cost function is to be minimized by another function (typically a constant), which plays the role of a constraint in the control model. We offer solutions to this problem using standard dynamic programming tools under the constrained discounted payoff criterion on an infinite horizon and the so-called principle of estimation and control. We used maximum likelihood estimators by means of a minimum least square error approximation in a pollution accumulation model to illustrate our results. One of the advantages of our approach compared to others is the intuition behind it: find optimal policies for an estimated version of the problem and let this estimation tend toward the real version of the problem. However, most risk analysts will not be as used to our methods as they are to, for instance, the model predictive control, MATLAB’s robust control toolbox, or the polynomial chaos expansion method, which have been used in the literature to address similar issues.

Keywords: consistent estimators; discounted cost; control with restrictions; maximum likelihood estimators; least square errors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/4/923/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/4/923/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:4:p:923-:d:1065492

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().