Introduction

Modeling age structures in continuous time typically involves partial or functional differential equations, which sharply departs from the traditional optimal control set-up. While a considerable literature exists on functional differential equations (from the seminal book of Bellman and Cooke, 1963), a relatively much smaller literature has been devoted so far to the optimal control of law of motions governed by such infinitely dimensioned equations. For example, in one of the recent books devoted to functional differential equations, co-authored by Kolmanovski and Myshkis (1999), only one chapter out of 16 actually deals with the optimal control of the latter (with an overwhelming part on the linear-quadratic case). In the optimal control of partial differential equations, numerous theoretical aspects are covered much better than applications to real-life problems, especially on real data. This book is a contribution to the scarce literature on the optimal control of age-structured populations, with applications to economics, demography, and ecology notably. More precisely, we gather a new material accounting for several crucial aspects of age-structured problems, not yet tackled in the related literature. This mainly concerns the following areas.