No-regret Control for a degenerate population model in divergence form with missing birth rate: a nonlinear case

Mohamed Sana; Somdouda Sawadogo; Sadou Tao

doi:10.14419/ijamr.v11i2.32104

Article Details

No-regret Control for a degenerate population model in divergence form with missing birth rate: a nonlinear case

Authors:

Mohamed Sana | Somdouda Sawadogo | Sadou Tao

Publisher:

Science Publishing Corporation

Journal:

International Journal of Applied Mathematical Research Vol.11 Issue 2, pp.14-34

Document Type:

Article

Publication Date:

8/2022

Document Language:

English

Document ID (Org No.):

2001386844

pISSN:

2227-4324

DOI:

10.14419/ijamr.v11i2.32104

Keywords:

Population dynamics

Abstract:

 We deal with a degenerate population equation in divergence form depending on time, on age and on space. In this model, the birth rate is unknown. We focus on the No-regret control and on the Low-regret control concepts of J. L. Lions treated in [ContrÃ´le Ã  moindres regrets des systÃ¨mes distribuÃ©s, C. R. Acad. Sci.Paris Ser. I Math., SIAM J. Control Optim. ,1992, Vol 315, pp. 1253â€“1257] and in [Duality arguments for multi-agents least regret control, Institut de France, 1999] to treat the problem. For this purpose, we prove first the existence of the Low-regret control and the No-regret control. And we use a suitable Hilbert space to show that the No-regret control is the limit of a family of adapted Low-regret controls defined by a quadratic pertubation and previously used by Nakoulima et al. in [Perturbations Ã  moindres regrets dans les systÃ¨mes distribuÃ©s Ã  donnÃ©es manquantes, C. R. Acad. Sci.Paris Ser. I Math., 2000, Vol 330, pp. 801â€“806]. Then we give a singular optimality system for the family of adapted Low-regret controls and for the No-regret control.

Article Details

No-regret Control for a degenerate population model in divergence form with missing birth rate: a nonlinear case

Authors: Mohamed Sana | Somdouda Sawadogo | Sadou Tao

Publisher: Science Publishing Corporation

Journal: International Journal of Applied Mathematical Research Vol.11 Issue 2, pp.14-34

Document Type: Article

Publication Date: 8/2022

Document Language: English

Document ID (Org No.): 2001386844

pISSN: 2227-4324

DOI: 10.14419/ijamr.v11i2.32104

Population dynamics

Issues

Authors:

Mohamed Sana | Somdouda Sawadogo | Sadou Tao

Publisher:

Science Publishing Corporation

Journal:

International Journal of Applied Mathematical Research Vol.11 Issue 2, pp.14-34

Document Type:

Article

Publication Date:

8/2022

Document Language:

English

Document ID (Org No.):

2001386844

pISSN:

2227-4324

DOI:

10.14419/ijamr.v11i2.32104