Hierarchic Control for a Two-Stroke Linear System with Missing Data
Ferdinand NIKIEMA *
Département de Mathématiques, Laboratoire d’Analyse Numériques d’Informatiques et de Biomathématiques, Université Joseph KI ZERBO, 03 BP 7021, Burkina Faso.
Mifiamba SOMA
Département de Mathématiques, (Centre Universitaire de Tenkodogo), Université Thomas SANKARA, Burkina Faso.
Moumini KERE
Département de Mathématiques (Institut Science et Technologie), Ecole Normale Supérieure, 01 BP 1757 ouaga 01, Burkina Faso.
Somdouda SAWADOGO
Département de Mathématiques (Institut Science et Technologie), Ecole Normale Supérieure, 01 BP 1757 ouaga 01, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we study a new hierarchical control problem for a linear two-stroke missing data problem, adjoint to an age and space structured single species population dynamics problem. We show that there are two controls such that the first control, called the follower, solves an optimal control problem which consists in bringing the state of the two-stroke linear system to a desired state, and the second control, called the leader, solves a null controllability problem. The results are obtained by means of an observability inequality associated with a homogeneous Dirichlet boundary condition.
Keywords: FOptimal control, carleman inequality, null controllability, missing data, population dynamics, low regret control, euler- lagrange formula