Hierarchical Stackelberg Control for a Two-Stroke Linear System in Population Dynamics
Ferdinand Nikiema *
Departement de mathematiques, Laboratoire d'Analyse Numeriques d'Informatiques et de Biomathematiques, Universite Joseph KI ZERBO, 03BP 7021E, Burkina Faso.
Moumini Kere
Departement de mathematiques, (Institut Science et Technologie), Ecole Normale Superieure, 01 BP 1757 ouaga 01, Burkina Faso.
Mifiamba Soma
Departement de mathematiques, (Centre Universitaire de tenkodogo), Universite Thomas Sankara, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
We study a unique hierarchical control problem for a two-stoke linear system, adjoint to an age and space dependent population dynamics problem. Using Stackelberg's method, we introduce two levels of control: a boundary control to achieve optimal flow regulation and a distributed control for null controllability. Our approach employs Carleman inequalities to address non-homogeneous Dirichlet boundary conditions, leading to new insights in controlling invasive species populations. These results highlight the applicability of hierarchical controls in ecological systems, providing a robust framework for future studies in control theory and population dynamics.
Keywords: Hierarchical stackelberg, stroke linear system, leadership model