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Scheduling of Controllers’ Update-Rates for Residual Bandwidth Utilization

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9884)

Abstract

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.

Keywords

  • 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.

This work is partially supported by the German Research Foundation (DFG) through the grant ZA 873/1-1.

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Notes

  1. 1.

    A square matrix A is called Hurwitz if the real parts of its eigenvalues are negative.

References

  1. Angeli, D., Sontag, E.D.: Forward completeness, unboundedness observability, and their Lyapunov characterizations. Syst. Control Lett. 38, 209–217 (1999)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    MathSciNet  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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. 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. 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)

    MathSciNet  CrossRef  Google Scholar 

  10. Green, M., Limebeer, D.J.N.: Linear Robust Control. Prentice Hall, Englewood Cliffs (1994)

    MATH  Google Scholar 

  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. Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall Inc., New Jersey (1996)

    Google Scholar 

  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. 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)

    MathSciNet  CrossRef  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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)

    CrossRef  Google Scholar 

  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 2015

    Google Scholar 

  20. Sontag, E.D.: Mathematical Control Theory, vol. 6, 2nd edn. Springer, New York (1998)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  22. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)

    MathSciNet  CrossRef  Google Scholar 

  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. 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)

    CrossRef  Google Scholar 

  25. Wiesbaden, S.A.M.: Autosar – The worldwide automotive standard for E/E systems. ATZextra worldwide 18(9), 5–12 (2013)

    Google Scholar 

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Correspondence to Majid Zamani .

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Zamani, M., Dey, S., Mohamed, S., Dasgupta, P., Mazo, M. (2016). Scheduling of Controllers’ Update-Rates for Residual Bandwidth Utilization. In: Fränzle, M., Markey, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2016. Lecture Notes in Computer Science(), vol 9884. Springer, Cham. https://doi.org/10.1007/978-3-319-44878-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-44878-7_6

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