Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Ellipsoidal Toolbox

Alex A. Kurzhanskiy and Pravin Varaiya

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2006-46
May 6, 2006

http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.pdf

Ellipsoidal Toolbox (ET) implements in MATLAB the ellipsoidal calculus and its application to the reachability analysis of continuous- and discrete-time, possibly time-varying linear systems, and linear systems with disturbances, for which ET calculates both open-loop and close-loop reach sets. The ellipsoidal calculus provides the following benefits:


BibTeX citation:

@techreport{Kurzhanskiy:EECS-2006-46,
    Author = {Kurzhanskiy, Alex A. and Varaiya, Pravin},
    Title = {Ellipsoidal Toolbox},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2006},
    Month = {May},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.html},
    Number = {UCB/EECS-2006-46},
    Abstract = {Ellipsoidal Toolbox (ET) implements in MATLAB the ellipsoidal calculus and its application
to the reachability analysis of continuous- and discrete-time, possibly time-varying linear
systems, and linear systems with disturbances, for which ET calculates both open-loop and
close-loop reach sets. The ellipsoidal calculus provides the following benefits:
<UL>
<LI>The complexity of the ellipsoidal representation is quadratic in the dimension of the state
space, and linear in the number of time steps.
<LI>It is possible to exactly represent the reach set of linear system through both external and
internal ellipsoids.
<LI>It is possible to single out individual external and internal approximating ellipsoids that are
optimal to some given criterion (e.g. trace, volume, diameter), or combination of such criteria.
<LI>It gives simple analytical expressions for the control that steers the state to a desired target.
</UL>}
}

EndNote citation:

%0 Report
%A Kurzhanskiy, Alex A.
%A Varaiya, Pravin
%T Ellipsoidal Toolbox
%I EECS Department, University of California, Berkeley
%D 2006
%8 May 6
%@ UCB/EECS-2006-46
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.html
%F Kurzhanskiy:EECS-2006-46