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Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants

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Theories of Programming and Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8051))

Abstract

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in invariant generation, which are both supported by modern numerical solvers.

This work has been supported in part by the projects NSFC-91118007, National Science and Technology Major Project of China (Grant No. 2012ZX01039-004), NSF CCF 1248069 and NSF DMS 1217054.

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Authors and Affiliations

  1. State Key Lab. of Comput. Sci., Institute of Software, CAS, Beijing, China

    Hengjun Zhao & Naijun Zhan

  2. University of Chinese Academy of Sciences, Beijing, China

    Hengjun Zhao

  3. Dept. of Comput. Sci., University of New Mexico, Albuquerque, NM, USA

    Deepak Kapur

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  1. Hengjun Zhao
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  2. Naijun Zhan
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  3. Deepak Kapur
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  1. International Institute for Software Technology, United Nations University, P.O. Box 3058, Macau, China

    Zhiming Liu

  2. Department of Computer Science, University of York, Deramore Lane, YO10 5GH, York, UK

    Jim Woodcock

  3. Software Engineering Institute, East China Normal University, 3663 Zhongshan Road (North), 200062, Shanghai, China

    Huibiao Zhu

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Zhao, H., Zhan, N., Kapur, D. (2013). Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants. In: Liu, Z., Woodcock, J., Zhu, H. (eds) Theories of Programming and Formal Methods. Lecture Notes in Computer Science, vol 8051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39698-4_22

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  • DOI: https://doi.org/10.1007/978-3-642-39698-4_22

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