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New results on the trade-off performance of LTI system with colored noise and encoder-decoder strategy. (English) Zbl 1423.93136

Summary: This paper studies the trade-off performance between tracking performance and control input energy of the multi-input multi-output (MIMO), linear and time-invariant (LTI) system over an additive coloured Gaussian noise (ACGN) channel and the encoder-decoder strategies. The restriction that filter in the encoder-decoder strategy must be diagonal matrix is not necessary. And some new results are derived according to the inner-outer factorization. The results show that the trade-off performance is correlated to the unstable pole, non-minimum phase zero of the system. Also new poles and zeros generated by the non-diagonal encoder-decoder strategies may affect the trade-off performance. At last, two examples with different filters and different encoder-decoder strategies are discussed to validate the conclusions. The various encoder-decoder strategies revealed by the simulations may enhance or deteriorate the trade-off performance proposed in this paper.

MSC:

93B55 Pole and zero placement problems
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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[1] Aguiar, A. P.; Hespanda, J. P.; Kokoroivć, P. V., Path-following for nonminimum phase systems removes performance limitations, IEEE Trans. Autom. Control, 50, 2, 234-239 (2005) · Zbl 1365.93213
[2] Braslavsky, J. H.; Middleton, R. H.; Freudenberg, J. S., Feedback stabilization over signal-to-noise ratio constrained channels, IEEE Trans. Autom. Control, 52, 8, 1391-1403 (2007) · Zbl 1366.93489
[3] Chen, C.-Y.; Guan, Z.-H.; Chi, Z.; Wu, Y.; Liao, R.-Q.; Jiang, X.-W., Fundamental performance limitations of networked control systems with novel trade-off factors and constraint channels, J. Frankl. Inst., 354, 3120-3133 (2017) · Zbl 1364.93748
[4] Darrell, G., \(H_∞\) Performance Limitations for Problems with Sensor Time Delays (2008), University of Waterloo: University of Waterloo Waterloo, Ontario, Canada, . Ph.d thesis
[5] Ding, L.; Wang, H.-N.; Guan, Z.-H.; Chen, J., Tracking under additive white Gaussian noise effect, IET Control Theory Appl., 4, 11, 2471-2478 (2010)
[6] Ding, L.; Guan, Z.-H.; Hou-Neng, W., Tracking performance limitations of random signal in multivariable discrete-time systems, Acta Automatica Sinica, 36, 3, 446-449 (2010)
[7] Francis, B. A., A Course in \(H_∞\) Control Theory (1987), Springer-Verlag: Springer-Verlag Berlin, Germanny · Zbl 0624.93003
[8] Goodwin, G. C.; Salgado, M. E.; Yuz, J. I., Performance limitations for linear feedback systems in the presence of plant uncertainty, IEEE Trans. Autom. Control, 48, 8, 1312-1319 (2003) · Zbl 1364.93296
[9] Goodwin, G. C.; Quevedo, D. E.; Silva, E. I., Architectures and coder design for networked control systems, Automatica, 44, 1, 248-257 (2008) · Zbl 1138.93302
[10] Havre, K., Stuides on Controllability Analysis and Control Structure Design (1998), Norwegian University of Science and Technology: Norwegian University of Science and Technology Trondheim, . Ph.d thesis
[11] Article ID 93904, 12 pages. · Zbl 1229.93071
[12] Jiang, X.-W.; Hu, B.; Guan, Z.-H.; Zhang, X.-H.; Yu, L., Best achievable tracking performance for networked control systems with encoder-decoder, Inf. Sci., 305, 184-195 (2015) · Zbl 1360.93777
[13] Jiang, X.-W.; Guan, Z.-H., Optimal tracking performance for non-square plant model with input disturbance and feedback channel noises, J. Frankl. Inst., 352, 7, 2971-2984 (2015) · Zbl 1395.93229
[14] Liu, Q.; Chen, W.; Wang, Z.; Qiu, L., Stabilization of MIMO systems over multiple independent and memoryless fading noisy channels, IEEE Trans. Autom. Control (2018)
[15] Middleton, R. H.; Rojas, A. J.; Freudenberg, J. S.; Braslavsky, J. H., Feedback stabilization over a first order moving average Gaussian noise channel, IEEE Trans. Autom. Control, 54, 1, 163-167 (2009) · Zbl 1367.94254
[16] Peters, A. A.; Mario, E. S.; Silva, E. I., Performance bounds in linear control of unstable MIMO systems with pole location constraint, Syst. Control Lett., 57, 5, 392-399 (2008) · Zbl 1139.93321
[17] Rojas, A. J., Signal-to-noise ratio performance limitations for input disturbance rejection in output feedback control, Syst. Control Lett., 58, 5, 353-358 (2009) · Zbl 1159.93350
[18] Rojas, A. J.; Braslvasky, J. H.; Middleton, R. H., Fundamental limitations in control over a communication channel, Automatica, 44, 12, 3147-3151 (2008) · Zbl 1153.93394
[19] Seron, M. M.; Braslavsky, J. H.; Goodwin, G. C., Fundamental Limitations in Filtering and Control (1997), Springer Verlag: Springer Verlag Cambridge, London · Zbl 0865.93002
[20] Silva, E. I.; Goodwin, G. C.; Quevedo, D. E., Control system design subject to SNR constraints, Automatica, 46, 2, 428-436 (2010) · Zbl 1205.93169
[21] Silva, E. I.; Oyarzún, D. A.; Salgado, M. E., On structurally constrained \(H_2\) performance bounds for stable MIMO plant models, IET Control Theory Appl., 1, 4, 1033-1045 (2007)
[22] New Orleans, Louisiana USA.
[23] Skogestad, S.; Postlethwaite, I., Multivariable Feedback Control Analysis and Design (2005), John Wiley & Sons: John Wiley & Sons Hoboken, New Jersey · Zbl 0842.93024
[24] Sun, J.; Djouadi, S. M., Robust stabilization over communication channels in the presence of unstructured uncertainty, IEEE Transtract. Autom. Control, 54, 4, 830-834 (2009) · Zbl 1367.93592
[25] Toker, O.; Chen, J.; Qiu, L., Tracking performance limitations in LTI multivariable discrete-time systems, IEEE Trans. Circu. Syst. I Fund. Theory Appl., 49, 5, 657-670 (2002) · Zbl 1368.93351
[26] Wang, B.; Guan, Z.-H., Optimal tracking and two-channel disturbance rejection under control energy constraint, Automatica, 47, 4, 733-738 (2011) · Zbl 1245.93063
[27] Wang, B.; Guan, Z.; Yuan, F.; Zhan, X., Lower bound of tracking performance with finite control energy and channel energy constraint, J. Control Theory Appl., 11, 3, 409-414 (2013)
[28] Wang, B.; Zhang, D.; Guan, Z.; Hu, B.; Chen, C., Tracking performance bound with finite control energy and erasure channel energy constraint, Asian J. Control, 18, 3, 1119-1129 (2016) · Zbl 1348.90179
[29] Wu, J.; Zhou, Z.-J.; Zhan, X.-S.; Yan, H.-C.; Ge, M.-f., Optimal modified tracking performance for MIMO networked control systems with communication constraints, ISA Trans., 68, 14-21 (2017)
[30] Zhan, X.-S.; Guan, Z.-H.; Wu, J.; Zhang, X.-H.; Wu, B., Tracking performance limitation of multi-channel networked systems, Control Theory Appl., 30, 4, 503-507 (2013)
[31] Zhou, K.; Doyle, J. C.; Glover, K., Robust and Optimal Control (1995), Prentice Hall: Prentice Hall Upper Saddle River, NJ
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