This directory contains codes that were used in

  Elizabeth Ann Cross and Ian M. Mitchell, "Level Set Methods for
  Computing Reachable Sets of Systems with Differential Algebraic
  Equation Dynamics," submitted to the 2008 American Control
  Conference in September 2007.

Most of the code requires version 1.1 of the Toolbox of Level Set
Methods (ToolboxLS) by Ian M. Mitchell, which can be downloaded from

	 http://www.cs.ubc.ca/~mitchell/ToolboxLS

Most examples also require the presence of an <addPathToKernel> script
file in the directory above the one in which this README exists.
Normally this script can be a copy of the script
<Examples/addPathToKernel> from the toolbox download (after it has
been modified to point to your own Toolbox installation).

The files implement the scheme for approximating the reachable sets of
the two example systems on their respective constraint manifolds, as
described in section III of the paper above, as well as simulations of
the two example systems.

The codes perform the following tasks:

1) simulateToyDAE: Generates sample trajectories for the 2D toy DAE
   system.

2) simulateOneGen: Generates 3D sample trajectories for the 3D single
   machine-load bus example.  Two different models are available: the
   original DAE, or the equivalent ODE.  The constraint surface is
   also plotted.

3) projReachToy: Generates the backwards reachable tube for the toy
   example on the 1D constraint manifold using an HJ PDE.  Creates the
   figure from section III of the paper, using simulateToyDAE.m to
   generate the sample trajectories.

4) projReachOneGen: Generates the backwards reachable tube for the
   single machine-load bus example on its 2D constraint manifold using
   an HJ PDE.

5) figureProjOneGen: Creates the 2D reachable tube figure from section
   V of the paper, using projReachOneGen.m to generate the reach tube
   and simulateOneGen to generate the sample trajectories.

Unfortunately, the full dimensional scheme described in section IV of
the paper requires some features not yet available in ToolboxLS, so we
apologize that the code for the corresponding reachable tubes and
figures has consequently not been released.

Questions or comments can be sent to mitchell@cs.ubc.ca

Ian Mitchell
University of British Columbia
September 2007
