SIAM Journal on Control and Optimization, Vol.58, No.3, 1289-1313, 2020
OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH MISSING BIRTH RATE
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 Ser. 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:population dynamics;incomplete data;optimal control;no-regret control;low-regret control;Euler-Lagrange formula