Citation
Ioannis Filippidis, Richard Murray. "Strategy-Driven Partitioning into Switching Modes for Piecewise-Affine Systems with Continuous Environments". 53rd IEEE Conference on Decision and Control, IEEE, 15, December, 2014.

Abstract
We propose a methodology for abstracting discrete-time piecewise-affine systems influenced by additive continuous environment variables, to synthesize correct-byconstruction controllers from linear temporal logic specifications. The proposed algorithm partitions the environment domain into polytopes, considered as modes controlled by the environment. In each mode the environment variable is treated as a bounded disturbance for the system. Mode polytopes are iteratively enlarged while a strategy isomorphism between successive system partitions can be constructed. Isomorphisms are obtained by solving the stable marriage problem after proving that our case admits a unique solution. This leads to mapping high-level symbolic variables to equivalence classes of polytopes, instead of single polytopes as in other works. We thus avoid the need to merge partitions, which can create sliver polytopes, causing numerical problems during reachability computations. The approach enables using the same strategy over partitions that have an isomorphic subgraph relevant to the strategy. Reachability checks between neighboring partitions are used to reduce non-determinism introduced by switching and allow continuous restoration of discrete state. If bifurcations occur that prevent strategy reuse, then switched system game synthesis is performed, and a logic modeling formalism proposed that avoids trivial cyclic counterexamples.

Electronic downloads

• https://www.src.org/library/publication/p069869/. (Link to paper on SRC website.)
• http://www.cds.caltech.edu/~murray/preprints/fm14-cdc_s.pdf

• HTML

  Ioannis Filippidis, Richard Murray. <a
  href="http://www.terraswarm.org/pubs/299.html"
  >Strategy-Driven Partitioning into Switching Modes for
  Piecewise-Affine Systems with Continuous
  Environments</a>, 53rd IEEE Conference on Decision and
  Control, IEEE, 15, December, 2014.

• Plain text

  Ioannis Filippidis, Richard Murray. "Strategy-Driven
  Partitioning into Switching Modes for Piecewise-Affine
  Systems with Continuous Environments". 53rd IEEE
  Conference on Decision and Control, IEEE, 15, December, 2014.

• BibTeX

  @inproceedings{FilippidisMurray14_StrategyDrivenPartitioningIntoSwitchingModesForPiecewiseAffine,
      author = {Ioannis Filippidis and Richard Murray},
      title = {Strategy-Driven Partitioning into Switching Modes
                for Piecewise-Affine Systems with Continuous
                Environments},
      booktitle = {53rd IEEE Conference on Decision and Control},
      organization = {IEEE},
      day = {15},
      month = {December},
      year = {2014},
      abstract = {We propose a methodology for abstracting
                discrete-time piecewise-affine systems influenced
                by additive continuous environment variables, to
                synthesize correct-byconstruction controllers from
                linear temporal logic specifications. The proposed
                algorithm partitions the environment domain into
                polytopes, considered as modes controlled by the
                environment. In each mode the environment variable
                is treated as a bounded disturbance for the
                system. Mode polytopes are iteratively enlarged
                while a strategy isomorphism between successive
                system partitions can be constructed. Isomorphisms
                are obtained by solving the stable marriage
                problem after proving that our case admits a
                unique solution. This leads to mapping high-level
                symbolic variables to equivalence classes of
                polytopes, instead of single polytopes as in other
                works. We thus avoid the need to merge partitions,
                which can create sliver polytopes, causing
                numerical problems during reachability
                computations. The approach enables using the same
                strategy over partitions that have an isomorphic
                subgraph relevant to the strategy. Reachability
                checks between neighboring partitions are used to
                reduce non-determinism introduced by switching and
                allow continuous restoration of discrete state. If
                bifurcations occur that prevent strategy reuse,
                then switched system game synthesis is performed,
                and a logic modeling formalism proposed that
                avoids trivial cyclic counterexamples.},
      URL = {http://terraswarm.org/pubs/299.html}
  }
  

Posted by Barb Hoversten on 9 Apr 2014.
Groups: tools