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Optimal control data scheduling with limited controller-plant communication

  • Jiapeng Xu
  • Chenglin Wen
  • Daxing Xu
Research Paper

Abstract

This paper considers optimal control data scheduling for finite-horizon linear quadratic regulation (LQR) control of scalar systems with limited controller-plant communication. Both the single-system and multiple-system scenarios are studied. For the first scenario, we derive the necessary and sufficient condition for a comparison function to be positive. Using this condition, the optimality of an explicit schedule is extended from unstable systems in the existing work to general systems. For the second scenario, we are able to construct explicit optimal scheduling policies for three particular classes of problems. Numerical examples are provided to illustrate the proposed results.

Keywords

control data scheduling LQR control optimal schedule limited transmission energy multiple systems 

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. U1509203, 61333011, U1664264, 61603133).

References

  1. 1.
    Lee E A, Seshia S A. Introduction to Embedded Systems: a Cyber-Physical Systems Approach. LeeSeshia.org, 2015Google Scholar
  2. 2.
    Wang L Y, Guo G, Zhuang Y. Stabilization of NCSs by random allocation of transmission power to sensors. Sci China Inf Sci, 2016, 59: 067201CrossRefGoogle Scholar
  3. 3.
    Liu Q, Wang Z, He X, et al. Event-based distributed filtering with stochastic measurement fading. IEEE Trans Ind Informat, 2015, 11: 1643–1652CrossRefGoogle Scholar
  4. 4.
    Liu H, Guo D, Sun F. Object recognition using tactile measurements: kernel sparse coding methods. IEEE Trans Instrum Meas, 2016, 65: 656–665CrossRefGoogle Scholar
  5. 5.
    Liu H, Liu Y, Sun F. Robust exemplar extraction using structured sparse coding. IEEE Trans Neural Netw Learn Syst, 2015, 26: 1816–1821MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gaid M E M B, Cela A S, Hamam Y. Optimal real-time scheduling of control tasks with state feedback resource allocation. IEEE Trans Control Syst Tech, 2009, 17: 309–326CrossRefGoogle Scholar
  7. 7.
    Sui T, You K, Fu M. Optimal sensor scheduling for state estimation over lossy channel. IET Control Theory Appl, 2015, 9: 2458–2465MathSciNetCrossRefGoogle Scholar
  8. 8.
    He L, Han D, Wang X. Optimal periodic scheduling for remote state estimation under sensor energy constraint. IET Control Theory Appl, 2014, 8: 907–915MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations. IEEE Trans Autom Control, 2004, 49: 1453–1464MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    You K, Xie L. Minimum data rate for mean square stabilizability of linear systems with markovian packet losses. IEEE Trans Autom Control, 2011, 56: 772–785MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Wen S, Guo G. Control and resource allocation of cyber-physical systems. IET Control Theory Appl, 2016, 10: 2038–2048MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lu Z B, Guo G. Communications and control co-design: a combined dynamic-static scheduling approach. Sci China Inf Sci, 2012, 55: 2495–2507MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Guo G, Lu Z, Han Q L. Control with Markov sensors/actuators assignment. IEEE Trans Autom Control, 2012, 57: 1799–1804MathSciNetCrossRefGoogle Scholar
  14. 14.
    Joshi S, Boyd S. Sensor selection via convex optimization. IEEE Trans Signal Process, 2009, 57: 451–462MathSciNetCrossRefGoogle Scholar
  15. 15.
    Mo Y, Ambrosino R, Sinopoli B. Sensor selection strategies for state estimation in energy constrained wireless sensor networks. Automatica, 2011, 47: 1330–1338MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Imer O C, Başar T. Optimal control with limited controls. In: Proceedings of American Control Conference, Minneapolis, 2006. 298–303Google Scholar
  17. 17.
    Bommannavar P, Basar T. Optimal control with limited control actions and lossy transmissions. In: Proceedings of IEEE Conference Decision and Control, Cancun, 2008. 2032–2037Google Scholar
  18. 18.
    Lincoln B, Bernhardsson B. LQR optimization of linear system switching. IEEE Trans Autom Control, 2002, 47: 1701–1705MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Savage C O, La Scala B F. Optimal scheduling of scalar Gauss-Markov systems with a terminal cost function. IEEE Trans Autom Control, 2009, 54: 1100–1105MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Yang C, Shi L. Deterministic sensor data scheduling under limited communication resource. IEEE Trans Signal Process, 2011, 59: 5050–5056MathSciNetCrossRefGoogle Scholar
  21. 21.
    Ren Z, Cheng P, Chen J, et al. Optimal periodic sensor schedule for steady-state estimation under average transmission energy constraint. IEEE Trans Autom Control, 2013, 58: 3265–3271CrossRefGoogle Scholar
  22. 22.
    Ren Z, Cheng P, Chen J, et al. Dynamic sensor transmission power scheduling for remote state estimation. Automatica, 2014, 50: 1235–1242MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Howard S, Suvorova S, Moran B. Optimal policy for scheduling of Gauss-Markov systems. In: Proceedings of the 7th International Conference on Information Fusion, Stockholm, 2004. 888–892Google Scholar
  24. 24.
    La Scala B F, Moran B. Optimal target tracking with restless bandits. Digital Signal Process, 2006, 16: 479–487CrossRefGoogle Scholar
  25. 25.
    Cabrera J B D. A note on greedy policies for scheduling scalar Gauss-Markov systems. IEEE Trans Autom Control, 2011, 56: 2982–2986MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Shi L, Zhang H. Scheduling two Gauss-Markov systems: an optimal solution for remote state estimation under bandwidth constraint. IEEE Trans Signal Process, 2012, 60: 2038–2042MathSciNetCrossRefGoogle Scholar
  27. 27.
    Shi L, Yuan Y, Chen J. Finite horizon LQR control with limited controller-system communication. IEEE Trans Autom Control, 2013, 58: 1835–1841MathSciNetCrossRefGoogle Scholar
  28. 28.
    Horn R A, Johnson C R. Matrix Analysis. 2nd ed. Cambridge: Cambridge University Press, 2012. 493–504CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Systems Science and Control Engineering, School of AutomationHangzhou Dianzi UniversityHangzhouChina
  2. 2.College of Electrical and Information EngineeringQuzhou UniversityQuzhouChina

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