Premium
Controllability of nonlinear diffusion system
Author(s) -
Maidi Ahmed,
Corriou JeanPierre
Publication year - 2015
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.22030
Subject(s) - controllability , nonlinear system , mathematics , diffusion , class (philosophy) , partial differential equation , tangent , distributed parameter system , mathematical analysis , control theory (sociology) , computer science , control (management) , physics , geometry , quantum mechanics , artificial intelligence , thermodynamics
In this article, the semi‐group theory is exploited to study the controllability of a particular but important class of distributed parameter systems with a uniform distributed control variable. This class is described by a partial differential equation that characterizes the nonlinear diffusion phenomenon. The main idea consists of using the Cole–Hopf tangent transformation, under some assumptions, in order to derive an equivalent linear model of the nonlinear diffusion system. Then, the study of the controllability of the linear model, based on the semi‐group approach, allows us to conclude about the controllability of the nonlinear diffusion system. The study is illustrated by an application example.