Nonnegative control of finite-dimensional linear systems

Lohéac J, Trélat E, Zuazua E (2020)


Publication Type: Journal article

Publication year: 2020

Journal

DOI: 10.1016/j.anihpc.2020.07.004

Abstract

We consider the controllability problem for finite-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 finite 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 finite-difference spatial discretization of the one-dimensional heat equation with Dirichlet boundary controls, and we provide numerical simulations.

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APA:

Lohéac, J., Trélat, E., & Zuazua, E. (2020). Nonnegative control of finite-dimensional linear systems. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire. https://dx.doi.org/10.1016/j.anihpc.2020.07.004

MLA:

Lohéac, Jérôme, Emmanuel Trélat, and Enrique Zuazua. "Nonnegative control of finite-dimensional linear systems." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire (2020).

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