Positive controllability of positive dynamical systems

Abstract

The paper is devoted to a study of constrained controllability and controllability for linear dynamical systems if the controls are taken to be nonnegative. In analogy to the usual definition of controllability it is possible to introduce the concept of positive controllability. We concentrate on approximate positive controllability for linear infinite-dimensional dynamical systems when the values of controls are taken from a positive closed convex cone and the operator of the system is normal and has pure discrete point spectrum. Special attention is paid for positive infinite-dimensional linear dynamical systems. General approximate constrained controllability results are then applied for distributed parameter dynamical systems described by linear partial differential equations of parabolic type with different kinds of boundary conditions. Several remarks and comments on the relationships between different concepts of controllability are given. Finally, a simple numerical illustrative example is also presented.