Optimal Birth Control of Population Dynamics *

We study optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition a fixed final horizon are developed, and the time optimal control problem, the problem with target sets, and the infinite planning horizon case are investigated. 11 1989 Academic Press, Inc.