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Support for reset assignments #441

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schillic opened this issue Feb 3, 2019 · 1 comment
Closed

Support for reset assignments #441

schillic opened this issue Feb 3, 2019 · 1 comment
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@schillic
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schillic commented Feb 3, 2019

A special case of #273.

Two options:

  1. project reset dimensions to zero and add a singleton corresponding to the reset via Minkowski sum
  2. fully project reset dimensions away and take the Cartesian product with (generally several) singletons corresponding to the reset

Example: 2D, we want to reset the first variable to 3.

  1. \begin{pmatrix} 0 0 \\ 0 1 \end{pmatrix}x + \{\binom{3}{0}\}
  2. \{(3)\} \times \begin{pmatrix} 0 1 \end{pmatrix}x

Option 1) seems easier to implement because it does not care about the position of the resets.
Option 2) could be interesting if the projection is easy to obtain because the set is already Cartesian (e.g., a CartesianProductArray from the low-dimensional continuous-time reachability or a Hyperrectangle from a box approximation).

@schillic schillic added this to the ARCH19 milestone Feb 3, 2019
@mforets
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mforets commented Feb 8, 2019

The reset map was added in MathematicalSystems#55. Perhaps we need a new function to transform it to matrix form. Because its apply function does not apply 😄 to sets, since it assumes that x is a vector in y[index] = value... we may extend apply(m::ResetMap, x::LazySet) with the projection as you propose above.

@schillic schillic self-assigned this Feb 13, 2019
schillic added a commit that referenced this issue Feb 15, 2019
@schillic schillic removed this from the ARCH19 milestone Feb 23, 2019
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