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Robust hierarchic control for a population dynamics model with missing birth rate

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Abstract

In this paper, we study the hierarchic control problem for a linear system of a population dynamics model with an unknown birth rate. Using the notion of low-regret control and an adapted observability inequality of Carleman type, we show that there exist two controls such that, the first control called follower solves an optimal control problem which consists in bringing the state of the linear system to the desired state, and the second one named leader is supposed to lead the population to extinction at final time.

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Acknowledgements

The first author was supported by the Alexander von Humboldt foundation, under the programme financed by the BMBF entitled “German research Chairs.” The second author is grateful for the facilities provided by the German research Chairs. The third authors was supported by the German Academic Exchange Service (D.A.A.D) under the Scholarship Programme PhD AIMS-Cameroon. The authors would like to express their gratitude to the unknown referees for helpful advice.

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Authors and Affiliations

  1. African Institute for Mathematical Sciences (AIMS), P.O. Box 608, Limbe Crystal Gardens, Limbe, South West Region, Cameroon

    Gisèle Mophou

  2. Laboratoire LAMIA, Université des Antilles, Campus Fouillole, 97159, Pointe-à-Pitre, Guadeloupe

    Gisèle Mophou

  3. (FWI)- Laboratoire MAINEGE, Université Ouaga 3S, 06 BP 10347, Ouagadougou 06, Burkina Faso

    Gisèle Mophou

  4. Departement de Mathematics, Institut des Sciences (IDS), 01 BP 1757, Ouaga 01, Burkina Faso

    Moumini Kéré

  5. University of Dschang, BP 67, Dschang, West Region, Cameroon

    Lionel Landry Djomegne Njoukoué

Authors
  1. Gisèle Mophou
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  2. Moumini Kéré
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  3. Lionel Landry Djomegne Njoukoué
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Correspondence to Gisèle Mophou.

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Mophou, G., Kéré, M. & Njoukoué, L.L.D. Robust hierarchic control for a population dynamics model with missing birth rate. Math. Control Signals Syst. 32, 209–239 (2020). https://doi.org/10.1007/s00498-020-00260-0

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  • DOI: https://doi.org/10.1007/s00498-020-00260-0

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