Abstract

We consider a model of population dynamics with age dependence and spatial structure but unknown birth rate. Using the notion of low-regret [J.-L. Lions, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992), pp. 1253--1257], we prove that we can bring the state of the system to a desired state by acting on the system via a localized distributed control. We provide the optimality systems that characterize the low-regret control. Moreover, using an appropriate Hilbert space, we prove that the family of low-regret controls tends to a so-called no-regret control, which we, in turn, characterize.

Keywords

  1. population dynamics
  2. incomplete data
  3. optimal control
  4. no-regret control
  5. low-regret control
  6. Euler--Lagrange formula

MSC codes

  1. 49J20
  2. 92D25
  3. 93C41

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References

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J. -L. Lions, Contrôle à moindre regrets des systèmes distribués, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992), pp. 1253--1257.
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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1289 - 1313
ISSN (online): 1095-7138

History

Submitted: 29 April 2019
Accepted: 14 February 2020
Published online: 11 May 2020

Keywords

  1. population dynamics
  2. incomplete data
  3. optimal control
  4. no-regret control
  5. low-regret control
  6. Euler--Lagrange formula

MSC codes

  1. 49J20
  2. 92D25
  3. 93C41

Authors

Affiliations

Funding Information

Fog Research Institute : FRI-454
Bundesministerium für Bildung und Forschung https://doi.org/10.13039/501100002347
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : TPA05

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