Infinite-horizon linear-quadratic age-structured optimal control problem

Abstract

In this paper we show how to apply the sufficient conditions to a simple infinite-horizon linear-quadratic age-structured optimal control problem.Our approach is based on the current-value Hamiltonian and it leads us to study a linear system of PDEs.Using the standard theory of Riccati equation we can simplify this problem decoupling the system of PDEs.When the model is autonomous, this theory allows us to find the optimal equilibrium by a Riccati ODE.This approach can be the starting point to face linear-quadratic age-structured differential games.