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:
- The complexity of the ellipsoidal representation is quadratic in the dimension of the state space, and linear in the number of time steps.
- It is possible to exactly represent the reach set of linear system through both external and internal ellipsoids.
- 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.
- It gives simple analytical expressions for the control that steers the state to a desired target.
BibTeX citation:
@techreport{Kurzhanskiy:EECS-2006-46,
Author = {Alex A. Kurzhanskiy and Pravin Varaiya},
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}
}
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