Open AccessStabilizing A Reaction-Diffusion System Via Feedback Control
Author(s) -
Smaranda Dodea
Publication year - 2013
Publication title -
analele ştiinţifice ale universităţii "al.i. cuza" din iaşi. matematică
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.144
H-Index - 12
eISSN - 2344-4967
pISSN - 1221-8421
DOI - 10.2478/v10157-012-0032-9
Subject(s) - eigenvalues and eigenvectors , control theory (sociology) , position (finance) , operator (biology) , mathematics , reaction–diffusion system , diffusion , feedback control , principal (computer security) , principal component analysis , stability (learning theory) , elliptic operator , control (management) , computer science , mathematical analysis , control engineering , engineering , physics , repressor , artificial intelligence , chemistry , biochemistry , quantum mechanics , transcription factor , thermodynamics , statistics , finance , economics , gene , operating system , machine learning
A two-component reaction-diffusion system modelling a prey-predator system is considered. A necessary condition and a sufficient condition for the internal stabilizability to zero of one the two components of the solution while preserving the nonnegativity of both components have been established by Aniţa. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization corresponding to the indicated feedback control depends on the principal eigenvalue of a certain elliptic operator. A large principal eigenvalue leads to a fast stabilization. The first goal of this paper is to approximate this principal eigenvalue. The second goal is to derive a conceptual iterative algorithm to improve at each iteration the position of the support of the stabilizing control in order to get a faster stabilization.