This directory contains code to recreate the figures from
section 2 of

  Ian M. Mitchell and Shahab Kaynama, "An Improved Algorithm for
  Robust Safety Analysis of Sampled Data Systems" in HSCC 2015.

It requires the Toolbox of Level Set Methods; see the readme.txt file
in the parent directory for instructions.

The tasks of the functions in this directory are:

* tightViabilityKernelVisualize: A script to generate figure 1, which
  is demonstration that the new algorithm gets a tight answer for the
  problem from the NAHS paper.  Runs tightViabilityKernel to compute
  the viability kernel of this figure.

* tightViabilityKernel: Function that computes the sampled data
  viability kernel for NAHS example.

* jitterViabilityKernelVisualize: A script to generate figure 2.  The
  subplots in this figure were generated separately by manually
  modifying the delta_fixed and delta_jitter values in the script.
  Calls jitterViabilityKernelStep to compute the viability kernel.

* jitterViabilityKernelStep: Function that computes the sampled data
  viability kernel for the constraint which is shaped like a step
  function.  This version of the kernel was used in the paper
  submission.

* jitterViabilityKernelL: Should be the same as
  jitterViabilityKernelStep, except that the constraint set is shaped
  like a (horizontally flipped) "L".  Decided not to use this
  constraint in the paper because it did not demonstrate as rich a
  kernel as the step-shaped constraint.

Questions and bug reports (and any examples of the use of this
technique on other problems) can be send to mitchell@cs.ubc.ca

Ian M. Mitchell 
October 2014
