Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)

Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos, Carmen Geraldi Higuera-Chan, Francisco Alejandro Alaffita-Hernández

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1 Scopus citations

Abstract

This piece is a follow-up of the research started by the authors on the constrained optimal control problem applied to pollution accumulation. We consider a dynamic system governed by a diffusion process with multiple modes that depends on an unknown parameter. We will study the components of the model and their restrictions and propose a scheme to solve the problem in which it is possible to determine (adaptive) policies that maximize a suitable discounted reward criterion using standard dynamic programming techniques in combination with discrete estimation methods for the unknown parameter. Finally, we develop a numerical example to illustrate our results with a particular case of the method of minimum least square error approximation.

Original languageEnglish
Article number1045
JournalMathematics
Volume11
Issue number4
DOIs
StatePublished - 1 Feb 2023

Keywords

  • consistent estimators
  • discounted cost
  • least square errors
  • maximum likelihood estimators
  • multiple Markovian modes

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