access icon free Performance limits in the control of single-input linear time-invariant plants over fading channels

This study presents performance limitations in the control of single-input linear time-invariant plants when controlled over a fading channel. The authors consider two architectures where the controller is co-located with the sensors. In the first architecture, the authors assume that delayed controller to actuator channel state information is available at the controller. In the second architecture, the authors relax that assumption and thus no channel-state-information is exploited at the controller. The authors’ main result is a closed form expression for the minimal stationary plant output variance, which is achievable in each scenario, as an explicit function of channel statistics and plant characteristics. To derive our results, the authors first show that there exists an equivalence, in a second-order moment sense, between communication over a single fading channel and communication over an additive white noise channel subject to a stationary signal-to-noise ratio (SNR) constraint. Such equivalence is then exploited to state conditions for stabilisation, and to derive explicit performance limitations, as simple corollaries of known results in the literature on networked control subject to SNR constraints. Numerical examples are included to illustrate our findings.

Inspec keywords: delays; stability; actuators; white noise; sensors; control system analysis; linear systems

Other keywords: stabilisation; fading channels; plant characteristics; additive white noise channel; sensors; channel statistics; SNR; single-input linear time-invariant plant control; delayed controller; actuator channel state information; minimal stationary plant output variance; signal-to-noise ratio constraint; closed form expression; performance limitations

Subjects: Distributed parameter control systems; Control system analysis and synthesis methods; Stability in control theory

References

    1. 1)
      • 20. Leong, A.S., Dey, S., Anand, J.: ‘Optimal LQG control over continuous fading channels’. Proc. 18th IFAC World Congress, Milan, Italy, 2011.
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
      • 22. Pakshin, P.V.: ‘State estimation and control synthesis for discrete linear systems with additive and multiplicative noise’, Automation and Remote Control, 1978, 39, (4), pp. 526535.
    11. 11)
    12. 12)
      • 9. Goldsmith, A.: ‘Wireless Communications’ (Cambridge University Press, 2005).
    13. 13)
    14. 14)
    15. 15)
      • 24. Freudenberg, J.S., Middleton, R.H., Braslavsky, J.H.: ‘Stabilization with disturbance attenuation over a Gaussian channel’. Proc. 46th IEEE Conf. on Decision and Control, New Orleans, USA, 2007.
    16. 16)
    17. 17)
      • 32. Zhou, K., Doyle, J.C., Glover, K.: ‘Robust and optimal control’ (Prentice-Hall, 1996).
    18. 18)
    19. 19)
    20. 20)
    21. 21)
    22. 22)
    23. 23)
      • 28. Silva, E.I., Pulgar, S.A.: ‘Performance limitations for SISO LTI plants controlled over SNR constrained channels’. Proc. of the 51st IEEE Conf. on Decision and Control, Maui, USA, December, 2012.
    24. 24)
      • 25. Li, Y., Tuncel, E., Chen, J., Su, W.: ‘Optimal tracking performance of discrete-time systems over an additive white noise channel’. Proc. 48th IEEE Conf. on Decision and Control and the 28th Chinese Control Conf., Shanghai, China, 2009.
    25. 25)
    26. 26)
      • 18. Chen, W., Zheng, J., Qiu, L.: ‘LQG control of LTI systems with random input and output gains’. Proc. of the 51st IEEE Conf. on Decision and Control, Maui, Hawaii, USA, 2012.
    27. 27)
      • 39. Freudenberg, J.S., Braslavsky, J.H., Middleton, R.H.: ‘Control over signal-to-noise ratio constrained channels: stabilization and performance’. Proc. 44th IEEE Conf. on Decission and Control and ECC, Sevilla, Spain, 2005.
    28. 28)
      • 17. Silva, E.I.: ‘A Unified Framework for the Analysis and Design of Networked Control SystemsPhD thesis, School of Electrical Engineering and Computer Science, University of Newcastle, Australia, 2009.
    29. 29)
    30. 30)
      • 30. Maass, A.I., Silva, E.I.: ‘Performance limitations in the control of LTI plants over fading channels’. Proc. Ninth Asian Control Conf., Istanbul, Turkey, June, 2013.
    31. 31)
    32. 32)
    33. 33)
    34. 34)
    35. 35)
    36. 36)
      • 41. Vargas, F.J., Chen, J., Silva, E.I.: ‘Necessary and sufficient conditions for mean square stabilization over MIMO SNR-constrained channels’. Proc. 51st IEEE Conf. on Decision and Control, Maui, USA, December, 2012.
    37. 37)
    38. 38)
    39. 39)
    40. 40)
    41. 41)
    42. 42)
    43. 43)
    44. 44)
    45. 45)
      • 42. Xiao, N., Xie, L.: ‘Analysis and design of discrete-time networked systems over fading channels’. Proc. 30th Chinese Control Conf., Yantai, China, 2011.
    46. 46)
      • 48. Cea, M., Goodwin, G.C., Wigren, T.: ‘Method and apparatuses for power control using variable step size’. US Patent 20,130,143,617, 6 June 2013.
    47. 47)
      • 35. Costa, O.L.V., Fragoso, M.D., Marques, R.P.: ‘Discrete time Markov jump linear systems’ (Springer, 2005).
    48. 48)
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