Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

The concept of Box Invariance for biologically-inspired dynamical systems

Alessandro Abate, Ashish Tiwari and S. Shankar Sastry

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2006-185
December 18, 2006

http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-185.pdf

In this paper we introduce a special notion of Invariance Set for certain classes of dynamical systems: the concept has been inspired by our experience with models drawn from Biology. We claim that Box Invariance, that is, the existence of ¿boxed¿ invariant regions, is a characteristic of many biologically-inspired dynamical models, especially those derived from stoichiometric reactions. Moreover, box invariance is quite useful for the verification of safety properties of such systems. This paper presents effective characterization of this notion for linear and affine systems, the study of the dynamical properties it subsumes, computational aspects of checking for box invariance, and a comparison with related concepts in the literature. The concept is illustrated using two models from biology.


BibTeX citation:

@techreport{Abate:EECS-2006-185,
    Author = {Abate, Alessandro and Tiwari, Ashish and Sastry, S. Shankar},
    Title = {The concept of Box Invariance for biologically-inspired dynamical systems},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2006},
    Month = {Dec},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-185.html},
    Number = {UCB/EECS-2006-185},
    Abstract = {In this paper we introduce a special notion of Invariance Set for certain classes of dynamical systems: the concept has been inspired by our experience with models drawn from Biology. We claim that Box Invariance, that is, the existence of ¿boxed¿ invariant regions, is a characteristic of many biologically-inspired dynamical models, especially those derived from stoichiometric reactions. Moreover, box invariance is quite useful for the verification of safety properties of such systems. This paper presents effective characterization of this notion for linear and affine systems, the study of the dynamical properties it subsumes, computational aspects of checking for box invariance, and a comparison with related concepts in the literature. The concept is illustrated using two models from biology.}
}

EndNote citation:

%0 Report
%A Abate, Alessandro
%A Tiwari, Ashish
%A Sastry, S. Shankar
%T The concept of Box Invariance for biologically-inspired dynamical systems
%I EECS Department, University of California, Berkeley
%D 2006
%8 December 18
%@ UCB/EECS-2006-185
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-185.html
%F Abate:EECS-2006-185