A Map-Reduce Parallel Approach to Automatic Synthesis of Control Software

  • Vadim Alimguzhin
  • Federico Mari
  • Igor Melatti
  • Ivano Salvo
  • Enrico Tronci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7976)


Many Control Systems are indeed Software Based Control Systems, i.e. control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of control software.

Available algorithms and tools (e.g., QKS) may require weeks or even months of computation to synthesize control software for large-size systems. This motivates search for parallel algorithms for control software synthesis.

In this paper, we present a Map-Reduce style parallel algorithm for control software synthesis when the controlled system (plant) is modeled as a discrete time linear hybrid system. Furthermore we present an MPI-based implementation PQKS of our algorithm. To the best of our knowledge, this is the first parallel approach for control software synthesis.

We experimentally show effectiveness of PQKS on two classical control synthesis problems: the inverted pendulum and the multi-input buck DC/DC converter. Experiments show that PQKS efficiency is above 60%. As an example, PQKS requires about 16 hours to complete the synthesis of control software for the pendulum on a cluster with 60 processors, instead of the 25 days needed by the sequential algorithm implemented in QKS.


Parallel Algorithm Abstract State Mixed Integer Linear Programming Inverted Pendulum Communication Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Henzinger, T.A., Sifakis, J.: The embedded systems design challenge. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 1–15. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Synthesis of quantized feedback control software for discrete time linear hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 180–195. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Model based synthesis of control software from system level formal specifications. ACM Trans. on Soft. Eng. and Meth. (to appear)Google Scholar
  4. 4.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Quantized feedback control software synthesis from system level formal specifications. CoRR abs/1107.5638v1 (2011)Google Scholar
  5. 5.
    Tomlin, C.J., Lygeros, J., Sastry, S.S.: Computing controllers for nonlinear hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 238–255. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Dean, J., Ghemawat, S.: Mapreduce: Simplified data processing on large clusters. In: OSDI, pp. 137–150 (2004)Google Scholar
  7. 7.
    Lin, J., Dyer, C.: Data-Intensive Text Processing with MapReduce. Synthesis Lectures on Human Language Technologies. Morgan & Claypool Publishers (2010)Google Scholar
  8. 8.
    Pacheco, P.: Parallel Programming with MPI. Morgan Kaufmann (1997)Google Scholar
  9. 9.
    Rodriguez, M., Fernandez-Miaja, P., Rodriguez, A., Sebastian, J.: A multiple-input digitally controlled buck converter for envelope tracking applications in radiofrequency power amplifiers. IEEE Trans. on Pow. El. 25(2), 369–381 (2010)CrossRefGoogle Scholar
  10. 10.
    Kreisselmeier, G., Birkhölzer, T.: Numerical nonlinear regulator design. IEEE Trans. on Automatic Control 39(1), 33–46 (1994)zbMATHCrossRefGoogle Scholar
  11. 11.
    Bryant, R.: Graph-based algorithms for boolean function manipulation. IEEE Trans. on Computers C-35(8), 677–691 (1986)CrossRefGoogle Scholar
  12. 12.
    Alimguzhin, V., Mari, F., Melatti, I., Salvo, I., Tronci, E.: Automatic control software synthesis for quantized discrete time hybrid systems. In: CDC, pp. 6120–6125. IEEE (2012)Google Scholar
  13. 13.
    So, W.C., Tse, C., Lee, Y.S.: Development of a fuzzy logic controller for dc/dc converters: design, computer simulation, and experimental evaluation. IEEE Trans. on Power Electronics 11(1), 24–32 (1996)CrossRefGoogle Scholar
  14. 14.
    Kim, W., Gupta, M.S., Wei, G.Y., Brooks, D.M.: Enabling on-chip switching regulators for multi-core processors using current staggering. In: ASGI (2007)Google Scholar
  15. 15.
    Alimguzhin, V., Mari, F., Melatti, I., Salvo, I., Tronci, E.: On model based synthesis of embedded control software. In: EMSOFT (2012)Google Scholar
  16. 16.
    Bemporad, A., Giorgetti, N.: A SAT-based hybrid solver for optimal control of hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 126–141. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Della Penna, G., Magazzeni, D., Tofani, A., Intrigila, B., Melatti, I., Tronci, E.: Automated Generation of Optimal Controllers through Model Checking Techniques. In: Cetto, J.A., Ferrier, J.-L., Costa dias Pereira, J.M., Filipe, J. (eds.) Informatics in Control Automation and Robotics. LNEE, vol. 15, pp. 107–119. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Della Penna, G., Magazzeni, D., Mercorio, F., Intrigila, B.: UPMurphi: A tool for universal planning on pddl+ problems. In: ICAPS (2009)Google Scholar
  19. 19.
    Mazo, M.J., Tabuada, P.: Symbolic approximate time-optimal control. Systems & Control Letters 60(4), 256–263 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Jha, S., Seshia, S.A., Tiwari, A.: Synthesis of optimal switching logic for hybrid systems. In: EMSOFT, pp. 107–116. ACM (2011)Google Scholar
  21. 21.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal: Status & developments. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 456–459. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  22. 22.
    Cassez, F., Jessen, J.J., Larsen, K.G., Raskin, J.-F., Reynier, P.-A.: Automatic synthesis of robust and optimal controllers – an industrial case study. In: Majumdar, R., Tabuada, P. (eds.) HSCC 2009. LNCS, vol. 5469, pp. 90–104. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Melatti, I., Palmer, R., Sawaya, G., Yang, Y., Kirby, R.M., Gopalakrishnan, G.: Parallel and distributed model checking in eddy. Int. J. Softw. Tools Technol. Transf. 11(1), 13–25 (2009)CrossRefGoogle Scholar
  24. 24.
    Bulychev, P.E., David, A., Larsen, K.G., Mikucionis, M., Legay, A.: Distributed parametric and statistical model checking. In: PDMC, pp. 30–42 (2011)Google Scholar
  25. 25.
    Barnat, J., Brim, L., Ceska, M., Rockai, P.: Divine: Parallel distributed model checker. In: PDMC. PDMC-HIBI 2010, pp. 4–7. IEEE Computer Society, Washington, DC (2010)Google Scholar
  26. 26.
    Schubert, W., Stengel, R.: Parallel synthesis of robust control systems. IEEE Trans. on Contr. Sys. Techn. 6(6), 701–706 (1998)CrossRefGoogle Scholar
  27. 27.
    Jurikovič, M., Čičák, P., Jelemenská, K.: Parallel controller design and synthesis. In: Proceedings of the 7th FPGAworld Conference, FPGAworld 2010, pp. 35–40. ACM, New York (2010)Google Scholar
  28. 28.
    Pardey, J., Amroun, A., Bolton, M., Adamski, M.: Parallel controller synthesis for programmable logic devices. Microprocessors and Microsystems 18(8), 451–457 (1994)CrossRefGoogle Scholar
  29. 29.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Linear constraints as a modeling language for discrete time hybrid systems. In: ICSEA. IARIA (2012)Google Scholar
  30. 30.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Synthesizing control software from boolean relations. Int. J. on Advances in SW 5(3&4), 212–223 (2012)Google Scholar
  31. 31.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Control software visualization. In: INFOCOMP. IARIA (2012)Google Scholar
  32. 32.
    Mari, F., Melatti, I., Salvo, I., Tronci, E.: Undecidability of quantized state feedback control for discrete time linear hybrid systems. In: Roychoudhury, A., D’Souza, M. (eds.) ICTAC 2012. LNCS, vol. 7521, pp. 243–258. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vadim Alimguzhin
    • 1
    • 2
  • Federico Mari
    • 1
  • Igor Melatti
    • 1
  • Ivano Salvo
    • 1
  • Enrico Tronci
    • 1
  1. 1.Computer Science DepartmentSapienza University of RomeItaly
  2. 2.Department of Computer Science and RoboticsUfa State Aviation Technical UniversityRussian Federation

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