--- _id: '7231' abstract: - lang: eng text: Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical systems without uncertainty. In this paper, we extend the approach with the ability to handle both continuous and hybrid dynamical systems with uncertainty that can reside in parameters and/or noise. We also improve the efficiency of the method significantly, by avoiding the use of interval-based methods for the enclosure-box computation without loosing soundness. We have developed a C++ prototype implementing the proposed approach and we evaluate it on several benchmarks. The experiments show that our approach is more efficient and precise than other methods in the literature. alternative_title: - LNCS article_processing_charge: No author: - first_name: Hui full_name: Kong, Hui id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87 last_name: Kong orcid: 0000-0002-3066-6941 - first_name: Ezio full_name: Bartocci, Ezio last_name: Bartocci - first_name: Yu full_name: Jiang, Yu last_name: Jiang - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 citation: ama: 'Kong H, Bartocci E, Jiang Y, Henzinger TA. Piecewise robust barrier tubes for nonlinear hybrid systems with uncertainty. In: 17th International Conference on Formal Modeling and Analysis of Timed Systems. Vol 11750. Springer Nature; 2019:123-141. doi:10.1007/978-3-030-29662-9_8' apa: 'Kong, H., Bartocci, E., Jiang, Y., & Henzinger, T. A. (2019). Piecewise robust barrier tubes for nonlinear hybrid systems with uncertainty. In 17th International Conference on Formal Modeling and Analysis of Timed Systems (Vol. 11750, pp. 123–141). Amsterdam, The Netherlands: Springer Nature. https://doi.org/10.1007/978-3-030-29662-9_8' chicago: Kong, Hui, Ezio Bartocci, Yu Jiang, and Thomas A Henzinger. “Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty.” In 17th International Conference on Formal Modeling and Analysis of Timed Systems, 11750:123–41. Springer Nature, 2019. https://doi.org/10.1007/978-3-030-29662-9_8. ieee: H. Kong, E. Bartocci, Y. Jiang, and T. A. Henzinger, “Piecewise robust barrier tubes for nonlinear hybrid systems with uncertainty,” in 17th International Conference on Formal Modeling and Analysis of Timed Systems, Amsterdam, The Netherlands, 2019, vol. 11750, pp. 123–141. ista: 'Kong H, Bartocci E, Jiang Y, Henzinger TA. 2019. Piecewise robust barrier tubes for nonlinear hybrid systems with uncertainty. 17th International Conference on Formal Modeling and Analysis of Timed Systems. FORMATS: Formal Modeling and Analysis of Timed Systems, LNCS, vol. 11750, 123–141.' mla: Kong, Hui, et al. “Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty.” 17th International Conference on Formal Modeling and Analysis of Timed Systems, vol. 11750, Springer Nature, 2019, pp. 123–41, doi:10.1007/978-3-030-29662-9_8. short: H. Kong, E. Bartocci, Y. Jiang, T.A. Henzinger, in:, 17th International Conference on Formal Modeling and Analysis of Timed Systems, Springer Nature, 2019, pp. 123–141. conference: end_date: 2019-08-29 location: Amsterdam, The Netherlands name: 'FORMATS: Formal Modeling and Analysis of Timed Systems' start_date: 2019-08-27 date_created: 2020-01-05T23:00:47Z date_published: 2019-08-13T00:00:00Z date_updated: 2023-09-06T14:55:15Z day: '13' department: - _id: ToHe doi: 10.1007/978-3-030-29662-9_8 external_id: arxiv: - '1907.11514' isi: - '000611677700008' intvolume: ' 11750' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.11514 month: '08' oa: 1 oa_version: Preprint page: 123-141 project: - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize publication: 17th International Conference on Formal Modeling and Analysis of Timed Systems publication_identifier: eissn: - 1611-3349 isbn: - 978-3-0302-9661-2 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Piecewise robust barrier tubes for nonlinear hybrid systems with uncertainty type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 11750 year: '2019' ...