Ellipsoidal Toolbox

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Ellipsoidal Toolbox

• Alex Kurzhanskiy
• Advisor
• professor Pravin Varaiya

• Homepage
• http//www.eecs.berkeley.edu/akurzhan/ellipsoids
• Description
• Ellipsoidal Toolbox is a standalone set of
  easy-to-use configurable MATLAB routines to
  perform operations with ellipsoids and
  hyperplanes of arbitrary dimensions. It computes
  the external and internal ellipsoidal
  approximations of geometric (Minkowski) sums and
  differences of ellipsoids, intersections of
  ellipsoids and intersections of ellipsoids with
  halfspaces and polytopes distances between
  ellipsoids, between ellipsoids and hyperplanes,
  between ellipsoids and polytopes and projections
  onto given subspaces.
• Ellipsoidal methods are used to compute forward
  and backward reach sets of continuous- and
  discrete-time piecewise affine systems. Forward
  and backward reach sets can be also computed for
  continuous-time piece-wise linear systems with
  disturbances. It can be verified if computed
  reach sets intersect with given ellipsoids,
  hyperplanes, or polytopes
• Software used by ET
• YALMIP high-level MATLAB toolbox for rapid
• development of
  optimization code
• http//control.ee.ethz.ch/joloef/yalmip.php
  
• SeDuMi MATLAB toolbox for solving optimization
• problems over symmetric
  cones
• http//sedumi.mcmaster.ca
• Both packages are included in the Ellipsoidal
  Toolbox distribution and need not be downloaded
  separately.

Reach Set Computation
Ellipsoidal Calculus
Affine transformation
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