Nonnegative control of finite-dimensional linear systems

Lohéac J, Trelat E, Zuazua E (2019)

Publication Language: English

Publication Type: Other publication type

Publication year: 2019

DOI: 10.1016/j.anihpc.2020.07.004

Abstract

We consider the controllability problem for nite-dimensional linear autonomous control systems with nonnegative controls. Despite the Kalman condition, the unilateral nonnegativity control constraint may cause a positive minimal controllability time. When this happens, we prove that, if the matrix of the system has a real eigenvalue, then there is a minimal time control in the space of Radon measures, which consists of a nite sum of Dirac impulses. When all eigenvalues are real, this control is unique and the number of impulses is less than half the dimension of the space. We also focus on the control system corresponding to a nite-dierence spatial discretization of the one-dimensional heat equation with Dirichlet boundary controls, and we provide numerical simulations.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Université de Lorraine FR France (FR) University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne FR France (FR)

How to cite

APA:

Lohéac, J., Trelat, E., & Zuazua, E. (2019). Nonnegative control of finite-dimensional linear systems.

MLA:

Lohéac, Jérome, Emmanuel Trelat, and Enrique Zuazua. Nonnegative control of finite-dimensional linear systems. 2019.

BibTeX: Download