Optimal Control of Insect Populations

We consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region Ω of the plane. We prove the existence of optimal paths and also deduce the first order necessary optimality conditions, using the Dubovitskii–Milyutin’s formalism, which leads to an iterative algorithm of the fixed-point kind. This problem may be considered as a model for the control of a mosquito population existing in a given region by using moving insecticide spreading devices. In this situation, an optimal control is any trajectory or path that must follow such spreading device in order to reduce the population as much as possible with a reasonable not too expensive strategy. We illustrate our results by presenting some numerical experiments

Optimal control and partial differential equations

In this work, some type of optimal control problems with equality constraints given by Partial Differential Equations (PDE) and convex inequality constraints are considered, obtaining their corresponding first order necessary optimality conditions by means of Dubovitskii-Milyutin (DM) method. Firstly, we consider problems with one objective functional (or scalar problems) but non-well posed equality constraints, where existence and uniqueness of state in function on control is not true (either one has existence but not uniqueness of state, or one has not existence of state for any control). In both cases, the classical Lions argument (re-writing the problem as an optimal control problem for the control without equality constraints, see for instance Lions, J. L. – Optimal Control of Systems Governed by Partial Differential Equations, Springer, 1970) can not be applied. Afterwards, we consider multiobjective problems (or vectorial problems), considering three different concepts of solution: Pareto, Nash and Stackelberg. In all cases, an adequate abstract DM method is developed followed by an example

An optimal control problem for a generalized Boussinesq model: The time dependent case

We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq approximation. We obtain the existence of the optimal control as well as first order optimality conditions of Pontryagin type by using the Dubovitskii-Milyutin formalism.Ministerio de Educación y CienciaConselho Nacional de Desenvolvimento Científico e TecnológicoFundação de Amparo à Pesquisa do Estado de São Paul