Citation
Alex A. Kurzhanskiy, Pravin Varaiya. "Ellipsoidal Toolbox". Technical report, EECS, UC Berkeley, 2006.

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: - 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.

Electronic downloads

• EECS-2006-46.pdf · application/pdf · 702 kbytes

• HTML

  Alex A. Kurzhanskiy, Pravin Varaiya. <a
  href="http://chess.eecs.berkeley.edu/pubs/93.html"
  ><i>Ellipsoidal Toolbox</i></a>,
  Technical report,  EECS, UC Berkeley, 2006.

• Plain text

  Alex A. Kurzhanskiy, Pravin Varaiya. "Ellipsoidal
  Toolbox". Technical report,  EECS, UC Berkeley, 2006.

• BibTeX

  @techreport{KurzhanskiyVaraiya06_EllipsoidalToolbox,
      author = {Alex A. Kurzhanskiy and Pravin Varaiya},
      title = {Ellipsoidal Toolbox},
      institution = {EECS, UC Berkeley},
      year = {2006},
      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: - 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. },
      URL = {http://chess.eecs.berkeley.edu/pubs/93.html}
  }
  

Posted by Alex A. Kurzhanskiy on 11 May 2006.
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