Optimality conditions for age-structured control systems

Abstract

We consider a fairly general model (extension of the Gurtin-MacCamy model of population dynamics) of an age structured control system with nonlocal dynamics and nonlocal boundary conditions. A necessary optimality condition is obtained in the form of Pontryagin's maximum principle, which is applicable to a number of practically meaningful models where the previously known results fail. We discuss such models (an epidemic control, and a capital accumulation model) as illustrations.

The reproductive value in distributed optimal control models

“…Applying the theory of DOCM (see Feichtinger et al (2003)) to the model (4), (5), (6) and (7) adjoint equation for the states and necessary first order conditions for the controls can be obtained. Solving the adjoint equation for N (a, t) with the method of characteristics together with the transversality condition ξ N (ω, t) = 0 we obtain 4…”

“…For the properties of the function f (·) and other functions to be introduced later on we refer to Feichtinger et al (2003) and references therein.…”

“…By applying the theory of DOCM (see Feichtinger et al (2003)) it is possible to derive necessary optimality conditions as well as a system for the adjoint variables for this problem.…”

Optimal investment models with vintage capital: Dynamic programming approach

“…The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11,12], [30,32]) either in cases when explicit solutions can be found or using Maximum Principle techniques.…”

“…The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11,12], [30,32]) either in cases when explicit solutions can be found or using Maximum Principle techniques.The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation.…”