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A Model-Based Approach to Testing Software Control Systems Described by Linear Differential Equations

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Advanced, Contemporary Control (PCC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 709))

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Abstract

The increasing complexity and wide applicability of software control systems requires the use of advanced and automated development and testing methodologies to meet time-to-market constraints, quality assurance and safety standards. In this context, the applicability of model-based development (MBD) and model-based testing (MBT) methodologies to such systems has gained attention in the last decade. The paper presents an integrated model-based approach to testing software control systems whose models are described by linear differential equations. The approach presented concerns conformance testing and includes the notation of tests, the implementation of a test comparator, the calculation of test coverage, the generation of test cases, and the execution of the tests. Finally, an example of a two-dimensional system is used for an experimental evaluation of the theoretical analysis and to present a perspective on the applicability of the approach for industrial projects.

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References

  1. Adrion, W., Brandstad, J., Cherniabsky, J.: Validation, verification and testing of computer software. Comput. Surv. 14(2), 159–192 (1982)

    Article  Google Scholar 

  2. Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V.: Optimal Control. Consultants Bureau, New York (1987)

    Book  MATH  Google Scholar 

  3. Boltyanskii, V.G.: Mathematical Methods of Optimal Control. Holt, Rinehart & Winston, New York (1971)

    Book  Google Scholar 

  4. Broy, M., Krcmar, H., Zimmermann, J., Kirstan, S.: EETimes Europe: model-based software development in the automotive industry (2011). http://www.electronics-eetimes.com/en/model-based-development.html

  5. Chilenski, J.J., Miller, S.P.: Applicability of modified condition/decision coverage to software testing. Softw. Eng. J. 9(5), 193–200 (1994)

    Article  Google Scholar 

  6. Dang, T.: Model-based testing of hybrid systems. In: Zander-Nowicka, J., Schieferdecker, I., Mosterman, P.J. (eds.) Model-Based Testing for Embedded Systems, pp. 383–423. CRC Press, Boca Raton (2011)

    Google Scholar 

  7. Dang, T., Nahhal, T.: Coverage-guided test generation for continuous and hybrid systems. Formal Methods Syst. Des. 34(2), 183–213 (2009)

    Article  MATH  Google Scholar 

  8. Engwerda, J.C., Otter, P.W.: On the choice of weighting matrices in the minimum variance controller. Automatica 25(2), 279–285 (1989)

    Article  MATH  Google Scholar 

  9. Esposito, J.M.: Automated test trajectory for hybrid systems. In: Proceedings of the 35th Southeastern Symposium on System Theory (2003)

    Google Scholar 

  10. Frankl, P.G., Weyuker, E.J.: An applicable family of data flow testing criteria. IEEE Trans. Softw. Eng. 34(10), 1483–1498 (1988)

    Article  MathSciNet  Google Scholar 

  11. Frehse, G., et al.: Spaceex: scalable verification of hybrid systems. In: Proceedings of the 23rd International Conference on Computer Aided Verification - CAV 2011, Snowbird, UT, USA (2011)

    Google Scholar 

  12. Ghoreishi, S.G., Nekoui, M.A., Basiri, S.O.: Optimal design of LQR weighting matrices based on intelligent optimization methods. Int. J. Intell. Inf. Process. 2(1), 63–74 (2011)

    Google Scholar 

  13. Girard, A., Le Guernic, C.: Efficient reachability analysis for linear systems using support functions. In: Proceedings of IFAC World Congress, Seoul, Korea (2008)

    Google Scholar 

  14. Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291–305. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31954-2_19

    Chapter  MATH  Google Scholar 

  15. Han, Z., Krogh, B.: Reachability analysis of hybrid control systems using reduced-order models. In: Proceedings of the 2004 Americal Control Conferenece, Boston, MA, USA (2004)

    Google Scholar 

  16. Howden, W.E.: Reliability of the path analysis testing strategy. IEEE Trans. Softw. Eng. 2(3), 208–215 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  17. International Electrotechnical Commission. International Standard IEC 61508. Functional safety of electrical/electronic/programmable electronic safety-related systems (2005). http://www.iec.ch/zone/fsafety

  18. Ioffe, A.D., Tikhomirov, V.M.: Theory of Extremal Problems. Elsevier, Amsterdam (1979)

    Google Scholar 

  19. ISTQB: International Software Testing Qualifications Board. Standard glossary of terms used in software testing, Version 2.1 (2010). http://www.astqb.org

  20. Julius, A., Fainekos, G.E., Anand, M., Lee, I., Pappas, G.: Robust test generation and coverage for hybrid systems. In: Proceedings of the 10th International Conference on Hybrid Systems: Computation and Control (HSCC), Pisa, Italy, April 2007, pp. 329–342 (2007)

    Google Scholar 

  21. Klamka, J.: Controllability of Dynamic Systems. WNT, Warsaw (1990)

    MATH  Google Scholar 

  22. LaValle, S.M., Kuffner, J.J.: Rapidly-exploring random trees: progress and prospects. In: Donald, B.R., Lynch, K.M., Rus, D. (eds.) Algorithmic and Computational Robotics: New Directions, pp. 293–308. A K Peters, Welleslay (2001)

    Google Scholar 

  23. Mitkowski, W.: Stabilization of Dynamic Systems. WNT, Warsaw (1991)

    MATH  Google Scholar 

  24. Ortega, M.G., Vargas, M., Castano, F., Rubio, F.R.: Improved design of the weighting matrices for the s/ks/t mixed sensitivity problem - application to a multivariable thermodynamic system. IEEE Trans. Control Syst. Technol. 14(1), 82–90 (2006)

    Article  Google Scholar 

  25. Skruch, P.: A coverage metric to evaluate tests for continuous-time dynamic systems. Cent. Eur. J. Eng. 1(2), 174–180 (2011)

    Google Scholar 

  26. Stavros, T., Dang, T.: Modeling, verification and testing usign timed and hybrid automata. In: Nicolescu, G., Mosterman, P.J. (eds.) Model-Based Design of Embedded Systems, pp. 383–436. CRC Press, Boca Raton (2009)

    Google Scholar 

  27. Tabuada, P.: Verification and Control of Hybrid Systems. Springer, Heidelberg (2009). https://doi.org/10.1007/978-1-4419-0224-5

    Book  MATH  Google Scholar 

  28. The Institute of Electrical and Electronics Engineers, Inc. IEEE standard glossary of software engineering terminology, IEEE Std 610.12-1990 (1990). http://www.standards.ieee.org

  29. Weiser, M.D., Gannon, J.D., McMullin, P.R.: Comparison of structural test coverage metrics. IEEE Softw. 2(2), 80–85 (1985)

    Article  Google Scholar 

  30. Zhu, H., Hall, P.A.V., May, J.H.R.: Software unit test coverage and adequacy. ACM Comput. Surv. (CSUR) 29(4), 366–427 (1997)

    Article  Google Scholar 

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Correspondence to Pawel Skruch .

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Skruch, P., Dlugosz, M., Mitkowski, W., Szelest, M. (2023). A Model-Based Approach to Testing Software Control Systems Described by Linear Differential Equations. In: Pawelczyk, M., Bismor, D., Ogonowski, S., Kacprzyk, J. (eds) Advanced, Contemporary Control. PCC 2023. Lecture Notes in Networks and Systems, vol 709. Springer, Cham. https://doi.org/10.1007/978-3-031-35173-0_21

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