Flow*: Taylor Model-Based Analyzer for Hybrid Systems

Flow*: Taylor Model-Based Analyzer for

Hybrid Systems


Please visit the new home page of Flow*.


What is Flow*?

Flow* (pronounced flowstar) is a tool which computes Taylor model flowpipes for continuous systems described by systems of non-linear Ordinary Differential Equations (ODEs), and hybrid systems that combine continuous evolution through ODEs with discrete jumps. Hybrid systems are useful to model the rich set of interactions between discrete controllers implemented in software/hardware and continuous plants modeled as ODEs. The current version of Flow* is able to handle hybrid systems with

  • continuous dynamics defined by non-linear ordinary differential equations (ODEs) which may have non-polynomial terms such as sine, cosine, square root and etc..
  • mode invariants and jump guards defined by conjunctions of polynomial constraints,
  • jump resets defined by polynomial mappings with uncertainties.

The tool also supports the ODEs with time-varying uncertain inputs which are bounded by intervals. The current version of Flow* is 1.2.0 which can be downloaded here.

What are flowpipes?p>There are various definitions on flowpipes. Here, a flowpipe means an over-approximation of the reachable states in a time interval (or step).

Why Taylor models?p>A Taylor model is the set defined by a polynomial over an interval domain and bloated by an interval. The flow of a continuous system can be tightly enclosed by Taylor models. With proper interval-based techniques, we may construct Taylor model flowpipes for non-linear hybrid systems.

How to use Flow*?p>The user’s manual for the previous version of Flow* can be found here. In the version 1.2.0, we slightly changed the modeling language, the new user’s manual can be found here.

Source codep>The source code is released under the GNU General Public License (GPL). We are happy to release the code under a license that is more (or less) permissive upon request.

Released versionsable border="1"> versions released dates new features 1.2.0 November 2013
 Non-polynomial ODEs with uncertain inputs,
improved intersection algorithm,
fast remainder refinement algorithm,
some bugs fixed.
1.0.0 May 2013
 Efficient algorithms on polynomial computation,
heuristics for efficiently selecting aggregation templates,
some bugs fixed.
0.9.0 October 2012 – Case studies>The case study homepage of Flow* can be found here. We collected a considerable number of non-trivial continuous and hybrid examples which are not only restricted to Flow*.

  • Xin Chen, Erika Abraham and Sriram Sankaranarayanan. Flow*: An Analyzer for Non-Linear Hybrid Systems. Computer Aided Verification (CAV), 2013.
  • Xin Chen, Erika Abraham and Sriram Sankaranarayanan. Taylor Model Flowpipe Construction for Non-linear Hybrid Systems. IEEE Real-Time Systems Symposium (RTSS), 2012.
  • Yan Zhang, Xin Chen, Erika Abraham and Sriram Sankaranarayanan. Empirical Taylor Model Flowpipe Construction for Analog Circuits (Abstract). Frontiers of Analog Computation Workshop, 2013. (slides will be posted soon).
  • Peoplel>
  • Xin Chen, RWTH Aachen University, Germany,
  • Erika Abraham, RWTH Aachen University, Germany.
  • Sriram Sankaranarayanan, University of Colorado, Boulder.
  • Acknowledgments>Xin Chen and Erika Abraham gratefully acknowledge support from the project HyPro of the German Research Council.

    Sriram Sankaranarayanan gratefully acknowledges support from NSF CAREER Award (Award # 0953941) and NSF CPS Award (Award # 1035845).

    References>Taylor models are a very useful computational tool from the interval analysis community. They were
    originally developed by Profs. Berz and Makino at the Michigan State University. They maintain a page with their Taylor Model related works here .