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

Abstract

The paper presents necessary optimality conditions of Pontryagin's type for infinite-horizon optimal control problems for age-structured systems with stateand 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.

Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time

“…This problem can be solved with age-structured optimal control theory [21][22][23] and established numerical methods [7].…”

“…The Maximum Principles in these papers, however, were specific to the problems. A general version of the Maximum Principle for age-structured optimal control models was first provided by Brokate [21], with [8,[22][23][24] adding further generalizations.…”

“…Equations (21) and (23) are the consumption Euler equations relating to stages 1 and 2, respectively. While (23) is of the standard form and requires no further discussion, (21) contains an additional term related to the shock.…”

Distributed optimal control models in environmental economics: a review

“…In both papers the time horizon is finite. The case of infinite horizon is investigated in Skritek and Veliov [68].…”

“…An alternative approach is to build on the papers Aseev et al [11,12], where the "right" adjoint function is explicitly specified in the ODE case. A step in this direction is the result in Skriteck and Veliov [68] for age-structured problems on infinite horizon.…”