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UTOPIC: Under-Approximation Through Optimal Control

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Quantitative Evaluation of Systems (QEST 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11785))

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Abstract

We consider a class of nonlinear systems of differential equations with uncertainties, i.e., with lack of knowledge in some of the parameters that is represented by a time-varying unknown bounded functions. An under-approximation of such systems consists of a subset of its reachable set, for any value of the unknown parameters. By relying on optimal control theory through Pontryagin’s principle, we provide an algorithm for the under-approximation of a linear combination of the state variables in terms of a fully automated tool-chain named UTOPIC. This allows to establish tight under-approximations of common benchmarks models with dimensions as large as sixty-five.

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Acknowledgement

Josu Doncel is supported by the Marie Sklodowska-Curie grant No. 777778, the Basque Government, Spain, Consolidated Research Group Grant IT1294-19, & the Spanish Ministry of Economy and Competitiveness project MTM2016-76329-R. Max Tschaikowski is supported by a Lise Meitner Fellowship funded by the Austrian Science Fund (FWF) under grant No. M-2393-N32 (COCO).

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Authors and Affiliations

  1. University of the Basque Country UPV/EHU, Leioa, Spain

    Josu Doncel

  2. Inria, Univ. Grenoble Alpes, Saint-Martin-d’Hères, France

    Nicolas Gast

  3. IMT School for Advanced Studies Lucca, Lucca, Italy

    Mirco Tribastone

  4. Technische Universität Wien, Wien, Austria

    Max Tschaikowski

  5. DTU Technical University of Denmark, Lyngby, Denmark

    Andrea Vandin

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  1. Josu Doncel
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  2. Nicolas Gast
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  4. Max Tschaikowski
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  5. Andrea Vandin
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Corresponding author

Correspondence to Max Tschaikowski .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    David Parker

  2. Saarland University, Saarbrücken, Germany

    Verena Wolf

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Doncel, J., Gast, N., Tribastone, M., Tschaikowski, M., Vandin, A. (2019). UTOPIC: Under-Approximation Through Optimal Control. In: Parker, D., Wolf, V. (eds) Quantitative Evaluation of Systems. QEST 2019. Lecture Notes in Computer Science(), vol 11785. Springer, Cham. https://doi.org/10.1007/978-3-030-30281-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-30281-8_16

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