OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH MISSING BIRTH RATE

Cyrille Kenne (1) , Günter Leugering (2) , Gisèle Mophou (3)

1 University of Buea
2 Department Mathematik [Erlangen]
3 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]

We consider a model of population dynamics with age dependence and spatial structure but unknown birth rate. Using the notion of Low-regret, we prove that we can bring the state of the system to desired state by acting on the system via a distributed control. Actually, we give the optimality systems that characterize the Low-regret control. Then we prove using an appropriate Hilbert space that the Low-regret control which is a family of controls tends to a control called No-regret control that we characterize.

Mots clés: Population dynamics; Low-regret control; incomplete data; Euler-Lagrange formula; optimal control; No-regret control

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Cyrille Kenne, Günter Leugering, Gisèle Mophou. OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH MISSING BIRTH RATE. SIAM Journal on Control and Optimization, In press. ⟨hal-02093551⟩