Davide Bresolin
ABSTRACT
Hybrid Systems are systems having a mixed discrete and continuous behaviour that cannot be characterized faithfully using either only discrete or only continuous models. A good framework for hybrid systems should support their compositional description and analysis, since commonly systems are specified by a composition of smaller subsystems, to cope with the complexity of their monolithic representation. Moreover, since the reachability problem for hybrid systems is undecidable, one should investigate the conditions that guarantee approximate computability of composition, when only approximations to the exact problem data are available.
In this paper, we propose an automata-based formalism (HIOA) for hybrid systems that is compositional and for which the evolution can be computed approximately. The main results are that the composition of compatible HIOA yields a pre-HIOA; a dominance result on the composition of HIOA by which we can replace any component in a composition by another one that exhibits the same external behaviour without affecting the behaviour of the composition; finally, the key result that the composition of two compatible upper(lower)-semicontinuous HIOA is a computable upper(lower)-semicontinuous pre-HIOA, which entails that the evolution of the composition is upper(lower)-semicomputable. A discussion on how compositionality/computability are handled in state-of-art libraries for reachability analysis closes the paper.
- D.E. Nadales Agut, D.A. van Beek, and J.E. Rooda. 2013. Syntax and semantics of the compositional interchange format for hybrid systems. The Journal of Logic and Algebraic Programming 82, 1 (2013), 1 -- 52. Google Scholar
Cross Ref
- Rajeev Alur, Radu Grosu, Insup Lee, and Oleg Sokolsky. 2006. Compositional modeling and refinement for hierarchical hybrid systems. Journal of Logic and Algebraic Programming 68, 1-2 (2006), 105--128. Google ScholarCross Ref
- Rajeev Alur and Thomas Henzinger. 1997. Modularity for timed and hybrid systems. In CONCUR '97: Proceedings of the 8th International Conference on Concurrency Theory. Lecture Notes in Computer Science, Vol. 1243. Springer, Berlin, Heidelberg, 74--88.Google ScholarCross Ref
- E. Asarin, T. Dang, O. Maler, and O. Bournez. 2000. Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems. In Proceedings of Hybrid Systems: Computation and Control (HSCC'00) (Lecture Notes in Computer Science), Vol. 1790. Springer, Berlin, Heidelberg, 20--31.Google ScholarCross Ref
- L. Benvenuti, D. Bresolin, P. Collins, A. Ferrari, L. Geretti, and T. Villa. 2014. Assume-guarantee verification of nonlinear hybrid systems with Ariadne. Int. J. Robust. Nonlinear Control 24, 4 (2014), 699--724. Google ScholarCross Ref
- O. Botchkarev and S. Tripakis. 2000. Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations. In Proceedings of Hybrid Systems: Computation and Control (HSCC'00) (LNCS), Vol. 1790. Springer, Berlin, Heidelberg, 73--88.Google ScholarCross Ref
- Xin Chen, Sergio Mover, and Sriram Sankaranarayanan. 2017. Compositional Relational Abstraction for Nonlinear Hybrid Systems. ACM Trans. Embed. Comput. Syst. 16, 5s, Article 187 (Sept. 2017), 19 pages. Google ScholarDigital Library
- X. Chen and S. Sankaranarayanan. 2016. Decomposed Reachability Analysis for Nonlinear Systems. In 2016 IEEE Real-Time Systems Symposium (RTSS). IEEE, New York, NY, USA, 13--24. Google ScholarCross Ref
- X. Chen and S. Sankaranarayanan. 2016. Decomposed Reachability Analysis for Nonlinear Systems. In 2016 IEEE Real-Time Systems Symposium (RTSS). IEEE, New York, NY, USA, 13--24.Google Scholar
- A. Cimatti, S. Mover, and S. Tonetta. 2011. HyDI: A Language for Symbolic Hybrid Systems with Discrete Interaction. In 2011 37th EUROMICRO Conference on Software Engineering and Advanced Applications. IEEE, New York, NY, USA, 275--278. Google ScholarDigital Library
- Alessandro Cimatti, Marco Roveri, and Stefano Tonetta. 2015. HRELTL: A temporal logic for hybrid systems. Information and Computation 245 (2015), 54 -- 71. Google ScholarDigital Library
- P. Collins. 2005. Continuity and computability of reachable sets. Theoret. Comput. Sci. 341 (2005), 162--195.Google ScholarDigital Library
- Pieter Collins. 2008. Semantics and Computability of the Evolution of Hybrid Systems. Research Report MAS-R0801. CWI, Amsterdam, The Netherlands. ISSN 1386--3703.Google Scholar
- P. Collins. 2011. Semantics and Computability of the Evolution of Hybrid Systems. SIAM Journal on Control and Optimization 49, 2 (2011), 890--925. arXiv:https://doi.org/10.1137/080716955 Google ScholarDigital Library
- P. Collins, D. Bresolin, L. Geretti, and T. Villa. 2012. Computing the Evolution of Hybrid Systems Using Rigorous Function Calculus. In Proc. of the 4th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS12) (IFAC Proceedings Volumes), Vol. 45, Issue 9. Elsevier, Amsterdam, The Netherlands, 284--290.Google Scholar
- Pieter Collins and John Lygeros. 2005. Computability of finite-time reachable sets for hybrid systems. In Proceedings of the 44th IEEE Conference on Decision and Control. IEEE, New York, NY, USA, 4688--4693.Google ScholarCross Ref
- T. Dang and O. Maler. 1998. Reachability Analysis via Face Lifting. In Proceedings of Hybrid Systems: Computation and Control (HSCC'98) (LNCS), Vol. 1386. Springer, Berlin, Heidelberg, 96--109.Google Scholar
- A. Donze and G. Frehse. 2013. Modular, hierarchical models of control systems in SpaceEx. In 2013 European Control Conference, ECC 2013. IEEE, New York, NY, USA, 4244--4251.Google ScholarCross Ref
- Alexandre Donzé and Oded Maler. 2010. Robust Satisfaction of Temporal Logic over Real-Valued Signals. In FORMATS 2010: Formal Modeling and Analysis of Timed Systems (LNCS), Vol. 6246. Springer, Berlin, Heidelberg, 92--106.Google ScholarCross Ref
- Georgios E. Fainekos and George J. Pappas. 2009. Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410, 42 (2009), 4262 -- 4291. Google ScholarDigital Library
- L. Geretti, S. Živanović Gonzalez, P. Collins, D. Bresolin, and T. Villa. 2019. Rigorous Continuous Evolution of Uncertain Systems. In Proc. of NSV 2019: Numerical Software Verification (LNCS), Vol. 11652. Springer International Publishing, Cham, 60--75.Google Scholar
- N. Halbwachs, Y.-E. Proy, and P. Raymond. 1994. Verification of Linear Hybrid Systems by Means of Convex Approximations. In Static Analysis Symposium. Springer-Verlag, Berlin, Heidelberg, 223--237.Google Scholar
- Thomas Henzinger, Marius Minea, and Vinayak Prabhu. 2001. Assume-Guarantee Reasoning for Hierarchical Hybrid Systems. In Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol. 2034. Springer, Berlin, Heidelberg, 275--290.Google Scholar
- Thomas A. Henzinger, Peter W. Kopke, Anuj Puri, and Pravin Varaiya. 1998. What's Decidable about Hybrid Automata? J. Comput. System Sci. 57, 1 (1998), 94 -- 124. Google ScholarDigital Library
- Thomas A. Henzinger and Jean-François Raskin. 2000. Robust Undecidability of Timed and Hybrid Systems. In HSCC 2000: Hybrid Systems: Computation and Control (LNCS), Vol. 1790. Springer, Berlin, Heidelberg, 145--159.Google Scholar
- A. B. Kurzhanski and P. Varaiya. 2000. Ellipsoidal Techniques for Reachability Analysis. In Proceedings of Hybrid Systems: Computation and Control (HSCC'00) (LNCS), Vol. 1790. Springer, Berlin, Heidelberg, 202--214.Google ScholarCross Ref
- H. L. Lee, M. Althoff, S. Hoelldampf, M. Olbrich, and E. Barke. 2015. Automated generation of hybrid system models for reachability analysis of nonlinear analog circuits. In 20th Asia and South Pacific Design Automation Conference, ASP-DAC 2015. IEEE, New York, NY, USA, 725--730.Google ScholarCross Ref
- Nancy Lynch, Roberto Segala, and Frits Vaandrager. 2003. Hybrid I/O automata. Information and Computation 185, 1 (2003), 105 -- 157. Google ScholarDigital Library
- Nancy Lynch, Roberto Segala, Frits Vaandrager, and H. Weinberg. 1996. Hybrid I/O automata. In Hybrid Systems III. HS 1995 (LNCS), Vol. 1066. Springer, Berlin, Heidelberg, 496--510. 10.1007/BFb0020971. Google ScholarCross Ref
- P. Nuzzo, A. L. Sangiovanni-Vincentelli, D. Bresolin, L. Geretti, and T. Villa. 2015. A Platform-Based Design Methodology with Contracts and Related Tools for the Design of Cyber-Physical Systems. Proc. IEEE 103, 11 (2015), 2104--2132. Google ScholarCross Ref
- Alessandro Pinto, Luca Carloni, Roberto Passerone, and Alberto Sangiovanni-Vincentelli. 2006. Interchange Formats for Hybrid Systems: Abstract Semantics. In Hybrid Systems: Computation and Control (LNCS), Vol. 3927. Springer, Berlin, Heidelberg, 491--506. http://chess.eecs.berkeley.edu/pubs/101.htmlGoogle Scholar
- K. Ruohonen. 1996. An effective Cauchy-Peano existence theorem for unique solutions. Internat. J. Found. Comput. Sci. 7, 2 (1996), 151--160.Google ScholarCross Ref
- S. Schupp, E. Abraham, I. B. Makhlouf, and S. Kowalewski. 2017. HyPro: A C++ library of state set representations for hybrid systems reachability analysis. In Proc. of NFM 2017: NASA Formal Methods (LNCS), Vol. 10227. Springer, Berlin, Heidelberg, 288--294.Google Scholar
- B. I. Silva, O. Stursberg, B. H. Krogh, and S. Engell. 2001. An Assessment of the Current Status of Algorithmic Approaches to the Verification of Hybrid Systems. In Proceedings of the Fortieth IEEE Conference on Decision and Control (CDC '01). IEEE, New York, NY, USA, 2867--2874.Google Scholar
- The Ariadne Team. 2020. Ariadne: an open library for formal verification of cyber-physical systems. http://www.ariadne-cps.orgGoogle Scholar
- Stavros Tripakis, Christos Stergiou, Chris Shaver, and Edward A. Lee. 2013. A modular formal semantics for Ptolemy. Mathematical Structures in Computer Science 23, 4 (2013), 834--881. Google ScholarCross Ref
- D. A. van Beek, P. J. Collins, D. E. Nadales Agut, J. E. Rooda, and Schiffelers R. R. H. 2009. New Concepts In The Abstract Format Of the Compositional Interchange Format. In Proc. of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems (IFAC Proceedings Volumes), Vol. 42, Issue 17. Elsevier, Amsterdam, The Netherlands, 250--255.Google Scholar
- Klaus Weihrauch. 2000. Computable analysis. Springer-Verlag, Berlin. x+285 pages.Google ScholarDigital Library
Index Terms
- A computable and compositional semantics for hybrid automata
Recommendations
What's decidable about recursive hybrid automata?
HSCC '15: Proceedings of the 18th International Conference on Hybrid Systems: Computation and ControlRecursive hybrid automata generalize recursive state machines in a similar way as hybrid automata generalize state machines. Recursive hybrid automata can be considered as collection of classical hybrid automata with special states that correspond to ...
From hybrid data-flow languages to hybrid automata: a complete translation
HSCC '12: Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and ControlHybrid systems are used to model embedded computing systems interacting with their physical environment. There is a conceptual mismatch between high-level hybrid system languages like Simulink, which are used for simulation, and hybrid automata, the ...
Inclusion dynamics hybrid automata
Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning ...
Comments