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Testing Cyber-Physical Systems through Bayesian Optimization

Published:27 September 2017Publication History
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Abstract

Many problems in the design and analysis of cyber-physical systems (CPS) reduce to the following optimization problem: given a CPS which transforms continuous-time input traces in Rm to continuous-time output traces in Rn and a cost function over output traces, find an input trace which minimizes the cost. Cyber-physical systems are typically so complex that solving the optimization problem analytically by examining the system dynamics is not feasible. We consider a black-box approach, where the optimization is performed by testing the input-output behaviour of the CPS.

We provide a unified, tool-supported methodology for CPS testing and optimization. Our tool is the first CPS testing tool that supports Bayesian optimization. It is also the first to employ fully automated dimensionality reduction techniques. We demonstrate the potential of our tool by running experiments on multiple industrial case studies. We compare the effectiveness of Bayesian optimization to state-of-the-art testing techniques based on CMA-ES and Simulated Annealing.

References

  1. H. Abbas and G. Fainekos. 2012. Convergence proofs for Simulated Annealing falsification of safety properties. In Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on. IEEE, 1594--1601.Google ScholarGoogle Scholar
  2. T. Akazaki. 2016. Falsification of Conditional Safety Properties for Cyber-Physical Systems with Gaussian Process Regression. 439--446.Google ScholarGoogle Scholar
  3. R. Alur. 2015. Principles of Cyber-Physical Systems. The MIT Press. Google ScholarGoogle Scholar
  4. R. Alur, T. Feder, and T. A. Henzinger. 1996. The benefits of relaxing punctuality. J. ACM 43, 1 (1996), 116--146. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Y. Annpureddy, C. Liu, G. E. Fainekos, and S. Sankaranarayanan. 2011. S-TaLiRo: A tool for temporal logic falsification for hybrid systems. In TACAS 11 (Lecture Notes in Computer Science), Vol. 6605. Springer, 254--257. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. S. Bansal, R. Calandra, T. Xiao, S. Levine, and C. Tomlin. 2017. Goal-driven dynamics learning via Bayesian optimization. CoRR abs/1703.09260 (2017).Google ScholarGoogle Scholar
  7. M. Branicky. 1995. Studies in hybrid systems: modeling, analysis, and control. Ph.D. thesis, Massachusetts Institute of Technology. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. E. Brochu, V. M. Cora, and N. de Freitas. 2010. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. CoRR abs/1012.2599 (2010).Google ScholarGoogle Scholar
  9. A. D. Bull. 2011. Convergence rates of efficient global optimization algorithms. J. Mach. Learn. Res. 12 (Nov. 2011), 2879--2904. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. J. Deshmukh, X. Jin, J. Kapinski, and O. Maler. 2015. Stochastic local search for falsification of hybrid systems. In ATVA. Springer, 500--517.Google ScholarGoogle Scholar
  11. A. Donzé. 2010. Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems. Springer, 167--170. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. A. Donzé and O. Maler. 2010. Robust Satisfaction of Temporal Logic over Real-Valued Signals. Springer, 92--106. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. T. Dreossi, T. Dang, A. Donzé, J. Kapinski, X. Jin, and J. V. Deshmukh. 2015. Efficient Guiding Strategies for Testing of Temporal Properties of Hybrid Systems. Springer International Publishing, 127--142.Google ScholarGoogle Scholar
  14. B. Fabien. 1998. Some tools for the direct solution of optimal control problems. Advances in Engineering Software 29, 1 (1998), 45--61. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. G. Fainekos. 2015. Automotive control design bug-finding with the S-TaLiRo tool. In ACC 2015. 4096.Google ScholarGoogle ScholarCross RefCross Ref
  16. S. Grünewälder, J.-Y. Audibert, M. Opper, and J. Shawe-Taylor. 2010. Regret Bounds for Gaussian Process Bandit Problems. In AISTATS 2010. 273--280.Google ScholarGoogle Scholar
  17. N. Hansen. 2016. The CMA Evolution Strategy: A tutorial. CoRR abs/1604.00772 (2016).Google ScholarGoogle Scholar
  18. M. Huang, K. Zaseck, K. Butts, and I. Kolmanovsky. 2016. Rate-based model predictive controller for diesel engine air path: Design and experimental evaluation. IEEE Trans. on Control Systems Technology 99 (2016), 1--14.Google ScholarGoogle Scholar
  19. X. Jin, J. V. Deshmukh, J. Kapinski, K. Ueda, and K. Butts. 2014. Powertrain control verification benchmark. In HSCC’14. ACM, 253--262. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. W. B. Johnson and J. Lindenstrauss. 1984. Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics 26 (1984), 189--206.Google ScholarGoogle ScholarCross RefCross Ref
  21. D. R. Jones, C. D. Perttunen, and B. E. Stuckman. 1993. Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory and Applications 79, 1 (1993), 157--181.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. 1983. Optimization by simulated annealing. Science 220, 4598 (1983), 671--680.Google ScholarGoogle Scholar
  23. D. Lizotte, T. Wang, M. Bowling, and D. Schuurmans. 2007. Automatic gait optimization with Gaussian process regression. In IJCAI 07. 944--949. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. N. Mahendran, Z. Wang, F. Hamze, and N. D. Freitas. 2012. Adaptive MCMC with Bayesian optimization. In AISTATS-12), N. D. Lawrence and M. A. Girolami (Eds.), Vol. 22. 751--760.Google ScholarGoogle Scholar
  25. O. Maler and D. Nickovic. 2013. Monitoring properties of analog and mixed-signal circuits. STTT 15, 3 (2013), 247--268.Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. A. Marco, P. Hennig, J. Bohg, S. Schaal, and S. Trimpe. 2016. Automatic LQR tuning based on Gaussian process global optimization. In ICRA 16. 270--277.Google ScholarGoogle Scholar
  27. Mathworks. 2017. Simulink—Simulation and model-based design. https://www.mathworks.com/products/simulink.html.Google ScholarGoogle Scholar
  28. W. Messner and D. Tilbury. 2017. Control tutorials for MATLAB and Simulink. http://ctms.engin.umich.edu/CTMS/index.php?aux=Basics_Simulink% #27.Google ScholarGoogle Scholar
  29. M. J. D. Powell. 2009. The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report DAMTP2009/NA06. University of Cambridge.Google ScholarGoogle Scholar
  30. C. E. Rasmussen and C. K. I. Williams. 2006. Gaussian processes for machine learning. MIT Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. S. Sankaranarayanan and G. Fainekos. 2012. Falsification of temporal properties of hybrid systems using the cross-entropy method. In HSCC 12. ACM, 125--134. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. P. Tabuada. 2009. Verification and Control of Hybrid Systems - A Symbolic Approach. Springer. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Z. Wang, F. Hutter, M. Zoghi, D. Matheson, and N. De Freitas. 2016. Bayesian optimization in a billion dimensions via random embeddings. Journal of Artificial Intelligence Research 55, 1 (2016), 361--387. Google ScholarGoogle ScholarCross RefCross Ref
  34. Y. Xue and P. Bogdan. 2017. Constructing compact causal mathematical models for complex dynamics. In ICCPS’17. ACM, 97--107. Google ScholarGoogle ScholarDigital LibraryDigital Library

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              cover image ACM Transactions on Embedded Computing Systems
              ACM Transactions on Embedded Computing Systems  Volume 16, Issue 5s
              Special Issue ESWEEK 2017, CASES 2017, CODES + ISSS 2017 and EMSOFT 2017
              October 2017
              1448 pages
              ISSN:1539-9087
              EISSN:1558-3465
              DOI:10.1145/3145508
              Issue’s Table of Contents

              Copyright © 2017 ACM

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              Publication History

              • Published: 27 September 2017
              • Accepted: 1 July 2017
              • Revised: 1 June 2017
              • Received: 1 April 2017
              Published in tecs Volume 16, Issue 5s

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