On the Value of the Preexisting Knowledge in an Optimal Control of Pollution Emissions

Angelina Chebotareva; Su Shimai; Sophia Tretyakova; Ekaterina Gromova

doi:10.21638/11701/spbu31.2021.04

Authors

Angelina Chebotareva St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia https://orcid.org/0000-0001-6999-286X
Su Shimai St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia https://orcid.org/0000-0001-9023-0202
Sophia Tretyakova St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia https://orcid.org/0000-0003-3246-0426
Ekaterina Gromova St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia https://orcid.org/0000-0003-0290-8373

DOI:

https://doi.org/10.21638/11701/spbu31.2021.04

Abstract

For a classical differential game of pollution control, we consider how the possession of specific information would impact the payoff of some players compared to cases in which the knowledge of information is incomplete. To measure the resulting discrepancy, we use the notion of value of information (VoI). Specifically, we study two scenarios, one in which the role of knowledge about the terminal cost is studied, and the other one, in which we analyze the influence of knowledge about the exact value of the upper bound on control. For each case, we obtain explicit analytical expressions for the payoff functions. These functions are used to quantify the exact value of information.

Keywords:

differential game, pollution problems, value of information, optimal control and trajectory

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