Optimal control data scheduling with limited controller-plant communication


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.

This is a preview of subscription content, access via your institution.


  1. 1

    Lee E A, Seshia S A. Introduction to Embedded Systems: a Cyber-Physical Systems Approach. LeeSeshia.org, 2015

    Google 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: 067201

    Article  Google 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: 1643–1652

    Article  Google Scholar 

  4. 4

    Liu H, Guo D, Sun F. Object recognition using tactile measurements: kernel sparse coding methods. IEEE Trans Instrum Meas, 2016, 65: 656–665

    Article  Google Scholar 

  5. 5

    Liu H, Liu Y, Sun F. Robust exemplar extraction using structured sparse coding. IEEE Trans Neural Netw Learn Syst, 2015, 26: 1816–1821

    MathSciNet  Article  Google 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: 309–326

    Article  Google Scholar 

  7. 7

    Sui T, You K, Fu M. Optimal sensor scheduling for state estimation over lossy channel. IET Control Theory Appl, 2015, 9: 2458–2465

    MathSciNet  Article  Google 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: 907–915

    MathSciNet  Article  Google Scholar 

  9. 9

    Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations. IEEE Trans Autom Control, 2004, 49: 1453–1464

    MathSciNet  Article  MATH  Google 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: 772–785

    MathSciNet  Article  MATH  Google Scholar 

  11. 11

    Wen S, Guo G. Control and resource allocation of cyber-physical systems. IET Control Theory Appl, 2016, 10: 2038–2048

    MathSciNet  Article  Google 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: 2495–2507

    MathSciNet  Article  MATH  Google Scholar 

  13. 13

    Guo G, Lu Z, Han Q L. Control with Markov sensors/actuators assignment. IEEE Trans Autom Control, 2012, 57: 1799–1804

    MathSciNet  Article  Google Scholar 

  14. 14

    Joshi S, Boyd S. Sensor selection via convex optimization. IEEE Trans Signal Process, 2009, 57: 451–462

    MathSciNet  Article  Google Scholar 

  15. 15

    Mo Y, Ambrosino R, Sinopoli B. Sensor selection strategies for state estimation in energy constrained wireless sensor networks. Automatica, 2011, 47: 1330–1338

    MathSciNet  Article  MATH  Google Scholar 

  16. 16

    Imer O C, Başar T. Optimal control with limited controls. In: Proceedings of American Control Conference, Minneapolis, 2006. 298–303

    Google 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. 2032–2037

    Google Scholar 

  18. 18

    Lincoln B, Bernhardsson B. LQR optimization of linear system switching. IEEE Trans Autom Control, 2002, 47: 1701–1705

    MathSciNet  Article  MATH  Google 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: 1100–1105

    MathSciNet  Article  MATH  Google Scholar 

  20. 20

    Yang C, Shi L. Deterministic sensor data scheduling under limited communication resource. IEEE Trans Signal Process, 2011, 59: 5050–5056

    MathSciNet  Article  Google 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: 3265–3271

    Article  Google Scholar 

  22. 22

    Ren Z, Cheng P, Chen J, et al. Dynamic sensor transmission power scheduling for remote state estimation. Automatica, 2014, 50: 1235–1242

    MathSciNet  Article  MATH  Google 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. 888–892

    Google Scholar 

  24. 24

    La Scala B F, Moran B. Optimal target tracking with restless bandits. Digital Signal Process, 2006, 16: 479–487

    Article  Google Scholar 

  25. 25

    Cabrera J B D. A note on greedy policies for scheduling scalar Gauss-Markov systems. IEEE Trans Autom Control, 2011, 56: 2982–2986

    MathSciNet  Article  MATH  Google 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: 2038–2042

    MathSciNet  Article  Google Scholar 

  27. 27

    Shi L, Yuan Y, Chen J. Finite horizon LQR control with limited controller-system communication. IEEE Trans Autom Control, 2013, 58: 1835–1841

    MathSciNet  Article  Google Scholar 

  28. 28

    Horn R A, Johnson C R. Matrix Analysis. 2nd ed. Cambridge: Cambridge University Press, 2012. 493–504

    Book  Google Scholar 

Download references


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

Author information



Corresponding author

Correspondence to Chenglin Wen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, J., Wen, C. & Xu, D. Optimal control data scheduling with limited controller-plant communication. Sci. China Inf. Sci. 61, 012202 (2018). https://doi.org/10.1007/s11432-016-9073-y

Download citation


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