The optimal tracking performance of single-input-single-output networked control systems over limited communication channels is proposed in this paper. The signal-to-noise ratio (SNR) constrained of communication channel is considered. The tracking performance is measured by the energy of the error variance response between the output of the plant and the reference signal. The optimal tracking performance is obtained by applying the square error criterion and the spectral factorization technique. It is shown that the optimal tracking performance is constrained by the non-minimum phase zeros, the unstable poles of a given plant, the power spectral density of a given reference signal, and the SNR of a communication channel. The results obtained in this work explicitly show how the optimal tracking performance is limited by the communication parameters (SNR in this paper). Finally, computer simulations are performed to verify the analytical results.
BraslavskyJHMiddletonRHFreudenbergJS (2007) Feedback stabilization over signal-to-noise ratio constrained channels. IEEE Transactions on Automatic Control52: 1391–1403.
2.
ChenJHaraSChenG (2007) Best tracking and regulation performance under control energy constraint. IEEE Transactions on Automatic Control48: 1320–1336.
3.
ChenWQiuL (2013) Stabilization of networked control systems with multirate sampling. Automatica49: 1528–1537.
4.
DengWHFeiMRHuHS (2013) A linear matrix inequality approach to system stabilization over constrained channels. Transactions of the Institute of Measurement and Control7: 183–191.
5.
DingLWangHNGuanZH (2010) Tracking under additive white Gaussian noise effect. IET Control Theory & Applications4: 2471–2478.
6.
DuDJFeiMRJiaTG (2013) Modeling and stability analysis of MIMO networked control systems with multi-channel random packet losses. Transactions of the Institute of Measurement and Control7: 166–174.
7.
FeiMRDengWHLiK. (2012) Stabilisation of a class of networked control systems with stochastic properties. International Journal of Modelling, Identification and Control1: 1–7.
8.
FrancisBA (1987) A Course inControl Theory. New York, NY: Springer.
9.
FuMYXieLH (2005) The sector bound approach to quantized feedback control. IEEE Transactions on Automatic Control50: 1698–1711.
10.
GoodwinGCSilvaEIQuevedoDE (2010) Analysis and design of networked control systems using the additive noise model methodology. Asian Journal of Control12: 443–459.
11.
GuanZHZhanXSFengG (2012) Optimal tracking performance of MIMO discrete-time systems with communication constraints. International Journal of Robust and Nonlinear Control22: 1429–1439.
12.
GuoG (2010) Linear systems with medium access constraint and Markov actuator assignment. IEEE Transactions on Circuits and Systems I57: 2999–3010.
13.
GuoG (2011) A switching system approach to sensor and actuator assignment for stabilization via limited multi-packet transmitting channels. International Journal of Control84: 78–93.
14.
GuoGLuZBHanQL (2012) Control with Markov sensors/actuators assignment. IEEE Transactions on Automatic Control57: 1799–1804.
15.
GuoGJinH (2010) A switching system approach to actuator assignment with limited channels. International Journal of Robust and Nonlinear Control12: 1407–1426.
16.
LiYQTuncelEChenJ (2009) Optimal tracking over an additive white Gaussian noise channel. In: 2009 American control conference, St. Louis, MO, 10–12 June, pp. 4026–4031.
17.
LuZBGuoG (2012) Communications and control co-design: A combined dynamic-static scheduling approach. Science China: Information Sciences55: 2495–2507.
18.
NairGEvansR (2003) Exponential stabilizability of finite-dimensional linear systems with limited data rates. Automatica39: 1632–1637.
19.
RojasAJBraslavskyHMiddletonH (2008) Fundamental limitations in control over a communication channel. Automatica44: 3147–3151.
20.
SilvaEIPulgarSA (2013) Performance limitations for single-input LTI plants controlled over SNR constrained channels with feedback. Automatica49: 540–547.
21.
SilvaEIGoodwinGCQuevedoDE (2010) Control system design subject to SNR constraints. Automatica46: 428–436.
22.
SilvaEIQuevedoDEGoodwinGC (2008) Optimal controller design for networked control systems. In: Proceedings of the 17th world congress of the international federation of automatic control, Seoul, South Korea, 6–11 July, pp. 5167–5172.
23.
SongYXieJXFeiMR. (2013) Mean square exponential stabilization of networked control systems with Markovian packet dropouts. Transactions of the Institute of Measurement and Control35(1): 75–82.
24.
VidyasagarM (1988) Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press.
25.
WuDXWuJChenS (2010) Stability of networked control systems with polytypic uncertainty and buffer constraint. IEEE Transactions on Automatic Control55: 1202–1208.
26.
XiongJLLamJ (2009) Stabilization of linear systems over networks with bounded packet loss. Automatica43: 80–87.
27.
ZhanXSGuanZHLiaoRQ. (2012a) Optimal performance in tracking stochastic signal under disturbance rejection. Asian Journal of Control14: 1608–1616.
28.
ZhanXSGuanZHYuanFS. (2012b) Performance analysis of networked control systems with SNR constraint. International Journal of Innovative Computing, Information and Control8: 8287–8298.
29.
ZhouKMDoyleJC (1995) Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall.
