Scheduling of Controllers’ Update-Rates for Residual Bandwidth Utilization

  • Majid ZamaniEmail author
  • Soumyajit Dey
  • Sajid Mohamed
  • Pallab Dasgupta
  • Manuel MazoJr.
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9884)


We consider the problem of incorporating control tasks on top of a partially loaded shared computing resource, whose current task execution pattern is characterizable using a window based pattern. We consider that the control task to be scheduled is allowed to switch between multiple controllers, each with different associated sampling rate, in order to adjust its requirement of computational bandwidth as per availability. We provide a novel control theoretic analysis that derives a Timed Automata (TA) based specification of allowable switchings among the different controller options while retaining the asymptotic stability of the closed loop. Our scheduling scheme computes a platform level residual bandwidth pattern from individual task level execution patterns. We then leverage the TA based controller specification and the residual bandwidth pattern in order to synthesize a Linearly Priced Timed Automata for which the minimum cost reachability solution provides realizable multi-rate control schedules. The provided scheduler not only guarantees the asymptotic stability of the control loop but also increases the robustness and control performance of the implementation by maximizing the bandwidth utilization.


Control Task Bandwidth Utilization Switching Signal Electronic Control Unit Switching Sequence 
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.


  1. 1.
    Angeli, D., Sontag, E.D.: Forward completeness, unboundedness observability, and their Lyapunov characterizations. Syst. Control Lett. 38, 209–217 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Anta, A., Tabuada, P.: To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans. Autom. Control 55(9), 2030–2042 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J.M.T., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cervin, A., Velasco, M., Marti, P., Camacho, A.: Optimal online sampling period assignment: theory and experiments. IEEE Trans. Control Syst. Technol. 6(4), 902–910 (2011)CrossRefGoogle Scholar
  6. 6.
    Chakraborty, S., Künzli, S., Thiele, L.: A general framework for analysing system properties in platform-based embedded system designs. In: DATE, vol. 3, p. 10190 (2003)Google Scholar
  7. 7.
    D’Innocenzo, A., Weiss, G., Alur, R., Isaksson, A.J., Johansson, K.H., Pappas, G.J.: Scalable scheduling algorithms for wireless networked control systems. In: IEEE International Conference on Automation Science and Engineering, CASE, pp. 409–414. IEEE (2009)Google Scholar
  8. 8.
    Goswami, D., Masrur, A., Schneider, R., Xue, C.J., Chakraborty, S.: Multirate controller design for resource-and schedule-constrained automotive ECUs. In: Proceedings of the Conference on Design, Automation and Test in Europe, pp. 1123–1126. EDA Consortium (2013)Google Scholar
  9. 9.
    Greco, L., Fontanelli, D., Bicchi, A.: Design and stability analysis for anytime control via stochastic scheduling. IEEE Trans. Autom. Control 56(3), 571–585 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Green, M., Limebeer, D.J.N.: Linear Robust Control. Prentice Hall, Englewood Cliffs (1994)zbMATHGoogle Scholar
  11. 11.
    Hespanha, J.P., et al.: Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 3, pp. 2655–2660. IEEE (1999)Google Scholar
  12. 12.
    Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall Inc., New Jersey (1996)Google Scholar
  13. 13.
    Larsen, K.G.: Priced timed automata: theory and tools. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS, pp. 417–425 (2009)Google Scholar
  14. 14.
    Nešic, D., Teel, A., Carnevale, D.: Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems. IEEE Trans. Autom. Control 54(3), 619–624 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nešić, D., Teel, A.R., Kokotović, P.: Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Syst. Control Lett. 38(4), 259–270 (1999)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Quagli, A., Fontanelli, D., Greco, L., Palopoli, L., Bicchi, A.: Design of embedded controllers based on anytime computing. IEEE Trans. Ind. Inf. 6(4), 492–502 (2010)CrossRefGoogle Scholar
  17. 17.
    Raha, R., Hazra, A., Mondal, A., Dey, S., Chakrabarti, P.P., Dasgupta, P.: Synthesis of sampling modes for adaptive control. In: IEEE International Conference on Control System, Computing and Engineering (ICCSCE), pp. 294–299. IEEE (2014)Google Scholar
  18. 18.
    Rasmussen, J.I., Larsen, K.G., Subramani, K.: Resource-optimal scheduling using priced timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 220–235. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Sharifi-Kolarijani, A., Adzkiya, D., Mazo, M., Jr.: Symbolic abstractions for the scheduling of event-triggered control systems. In: Proceedings of 54st IEEE Conference on Decision and Control, Osaka, Japan, December 2015Google Scholar
  20. 20.
    Sontag, E.D.: Mathematical Control Theory, vol. 6, 2nd edn. Springer, New York (1998)Google Scholar
  21. 21.
    Sontag, E.D.: Input to state stability: basic concepts and results. In: Nistri, P., Stefani, G. (eds.) Nonlinear and Optimal Control Theory. Lecture Notes in Mathematics, vol. 1932, pp. 163–220. Springer, Berlin (2008)CrossRefGoogle Scholar
  22. 22.
    Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Thiele, L., Chakraborty, S., Naedele, M.: Real-time calculus for scheduling hard real-time systems. In: IEEE International Symposium on Circuits, Systems. Emerging Technologies for the 21st Century, vol. 4, pp. 101–104 (2000)Google Scholar
  24. 24.
    Weiss, G., Alur, R.: Automata based interfaces for control and scheduling. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 601–613. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Wiesbaden, S.A.M.: Autosar – The worldwide automotive standard for E/E systems. ATZextra worldwide 18(9), 5–12 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Majid Zamani
    • 1
    Email author
  • Soumyajit Dey
    • 2
  • Sajid Mohamed
    • 2
  • Pallab Dasgupta
    • 2
  • Manuel MazoJr.
    • 3
  1. 1.Technical University of MunichMunichGermany
  2. 2.Indian Institute of TechnologyKharagpurIndia
  3. 3.Delft University of TechnologyDelftThe Netherlands

Personalised recommendations