On the Infinite-Horizon Optimal Control of Age-Structured Systems

The paper presents necessary optimality conditions of Pontryagin's type for infinite-horizon optimal control problems for age-structured systems with state- and control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a "complete" set of optimality conditions is missing in the existing literature, because it is problematic to define in a sound way appropriate transversality conditions for the corresponding adjoint system. The main novelty is that (building on recent results by Aseev and the second author) the adjoint function in the Pontryagin principle is explicitly defined, which avoids the necessity of transversality conditions. The result is applied to several models considered in the literature.