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