© The Institution of Engineering and Technology
This article studies the problem of H ∞ dynamic output-feedback control of non-linear networked discrete-time systems with data packet dropouts. Specifically, the data missing happens randomly from the sensor to the controller and the controller to the actuator. A sequence of independent variables obeying the Bernoulli random binary distribution is introduced to account for the measurement missing. The Takagi–Sugeno fuzzy model is used to describe the non-linear plant. In addition, the strategy of parallel distributed compensation is adopted to design the fuzzy dynamic output-feedback controller. Here, attention is focused on obtaining the sufficient conditions to guarantee the closed-loop system to be stochastically stable as well as the prescribed H ∞ performance. An approach based on fuzzy Lyapunov function is developed to solve it. To tackle the non-convex problem, the cone-complementarity linearisation procedure is adopted. Finally, a numerical example is employed to show the usefulness of the proposed result.
References
-
-
1)
-
J.L. Xiong ,
J. Lam
.
Stabilization of networked control systems with a logic ZOH.
IEEE Trans. Autom. Control
,
2 ,
358 -
363
-
2)
-
M. Liu ,
D.W.C. Ho ,
Y. Niu
.
Stabilization of Markovian jump linear system over networks with random communication delay.
Automatica
,
2 ,
416 -
421
-
3)
-
38. Qiu, J., Feng, G., Gao, H.: ‘Fuzzy-model-based piecewise H∞ static-output-feedback controller design for networked nonlinear systems’, IEEE Trans. Fuzzy Syst., 2010, 18, (5), pp. 919–934 (doi: 10.1109/TFUZZ.2010.2052259).
-
4)
-
O.C. Imer ,
S. Yüksel ,
T. Başar
.
Optimal control of LTI systems over unreliable communication links.
Automatica
,
1429 -
1439
-
5)
-
Y. Zhao ,
H.J. Gao ,
J. Lam ,
B. Du
.
Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach.
IEEE Trans. Fuzzy Syst.
,
4 ,
750 -
762
-
6)
-
9. Azimi-Sadjadi, B.: ‘Stability of networked control systems in the presence of packet losses’. Proc. of 2003 IEEE Conf. Decision and Control, Citeseer, 2003, pp. 676–681.
-
7)
-
30. Mahmoud, M.S., Khan, G.D.: ‘Dynamic output feedback of networked control systems with partially known Markov chain packet dropouts’, Opt. Control Appl. Methods, 2013, .
-
8)
-
30. Li, H., Yu, J., Hilton, C., Liu, H.: ‘Adaptive sliding mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach’, IEEE Trans. Ind. Electron., 2013, 60, (8), pp. 3328–3338 (doi: 10.1109/TIE.2012.2202354).
-
9)
-
19. Karimi, H.R.: ‘Robust H∞ filter design for uncertain linear systems over network with network-induced delays and output quantization’, Model., Identif. Control, 2009, 30, (1), pp. 27–37 (doi: 10.4173/mic.2009.1.3).
-
10)
-
33. Hongli, D., Ho, D.W.C., Gao, H.: ‘Distributed H∞ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks’, IEEE Trans. Ind. Electron., 2013, 60, (10), pp. 4665–4672 (doi: 10.1109/TIE.2012.2213553).
-
11)
-
Y. Zhao ,
H. Gao ,
T. Chen
.
Fuzzy constrained predictive control of non-linear systems with packet dropouts.
IET Control Theory Appl.
,
9 ,
1665 -
1677
-
12)
-
6. Ishii, H., Francis, B.A.: ‘Limited data rate in control systems with networks’, (Springer, 2002), vol. 275.
-
13)
-
H.D. Tuan ,
P. Apkarian ,
T. Narikiyo ,
Y. Yamamoto
.
Parameterized linear matrix inequality techniques in fuzzy control system design.
IEEE Trans. Fuzzy Syst.
,
2 ,
324 -
332
-
14)
-
6. Zhang, J., Lam, J., Xia, J.: ‘Output feedback sliding mode control under networked environment’, Int. J. Syst. Sci., 2013, 44, (4), pp. 750–759 (doi: 10.1080/00207721.2011.618643).
-
15)
-
T. Takagi ,
M. Sugeno
.
Fuzzy identification of systems and its applications to modelling and control.
IEEE Trans. Syst. Man. Cybern.
,
1 ,
116 -
132
-
16)
-
Z. Mao ,
B. Jiang ,
P. Shi
.
H∞ fault detection filter design for networked control systems modelled by discrete Markovian jump systems.
IET Control Theory Appl.
,
8 ,
675 -
681
-
17)
-
G.C. Walsh ,
H. Ye ,
L.G. Bushnell
.
Stability analysis of networked control systems.
IEEE Trans. Control Syst. Technol.
,
438 -
446
-
18)
-
H.J. Gao ,
T.W. Chen ,
J. Lam
.
A new delay system approach to network-based control.
Automatica
,
39 -
52
-
19)
-
T.C. Yang ,
C. Peng ,
D. Yue ,
M.R. Fei
.
New study of controller design for networked control systems.
IET Control Theory Appl.
,
7 ,
403 -
412
-
20)
-
26. Rubió-Massegú, J., Rossell, J.M., Karimi, H.R., Palacios-Quiñonero, F.: ‘Static output-feedback control under information structure constraints’, Automatica, 2013, 49, (1), pp. 313–316 (doi: 10.1016/j.automatica.2012.10.012).
-
21)
-
H. Li ,
H. Liu ,
H. Gao ,
P. Shi
.
Reliable fuzzy control for active suspension systems with actuator delay and faults.
IEEE Trans. Fuzzy Syst.
,
2 ,
342 -
357
-
22)
-
H. Li ,
B. Chen ,
Q. Zhou ,
W. Qian
.
Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters.
IEEE Trans. Syst. Man Cybern. Part B
,
1 ,
94 -
102
-
23)
-
H. Dong ,
Z. Wang ,
D.W.C. Ho ,
H. Gao
.
Robust H∞ fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements.
IEEE Trans. Fuzzy Syst.
,
4 ,
712 -
725
-
24)
-
H. Gao ,
T. Chen
.
Stabilization of nonlinear systems under variable sampling: a fuzzy control approach.
IEEE Trans. Fuzzy Syst.
,
5 ,
972 -
983
-
25)
-
17. Yue, D., Tian, E., Wang, Z., Lam, J.: ‘Stabilization of systems with probabilistic interval input delays and its applications to networked control systems’, IEEE Trans. Syst. Man Cybern.-Part A: Syst. Humans, 2009, 39, (4), pp. 939–945 (doi: 10.1109/TSMCA.2009.2019875).
-
26)
-
R.A. Gupta ,
M.Y. Chow
.
Networked control system: overview and research trends.
IEEE Trans. Ind. Electron.
,
7 ,
2527 -
2535
-
27)
-
M. Sahebsara ,
T. Chen ,
S.L. Shah
.
Optimal H∞ filtering in networked control systems with multiple packet dropouts.
Syst. Control Lett.
,
9 ,
696 -
702
-
28)
-
22. Zhao, Y., Zhang, Z., Zhao, Y., Gao, H.: ‘Fault detection with network communication’, Int. J. Syst. Sci., 2010, 41, (8), pp. 947–956 (doi: 10.1080/00207720903180572).
-
29)
-
13. Jiang, B., Mao, Z., Shi, P.: ‘H∞-filter design for a class of networked control systems via T–S fuzzy-model approach’, IEEE Trans. Fuzzy Syst., 2010, 18, (1), pp. 201–208 (doi: 10.1109/TFUZZ.2009.2037009).
-
30)
-
25. Su, X., Shi, P., Wu, L., Song, Y.D.: ‘A novel approach to filter design for T–S fuzzy discrete-time systems with timevarying delay’, IEEE Trans. Fuzzy Syst., 2012, 20, (6), pp. 1114–1129 (doi: 10.1109/TFUZZ.2012.2196522).
-
31)
-
17. Izadi, I., Chen, T., Zhao, Q.: ‘Norm invariant discretization for sampled-data fault detection’, Automatica, 2005, 41, (9), pp. 1633–1637 (doi: 10.1016/j.automatica.2005.03.028).
-
32)
-
H. Dong ,
Z. Wang ,
H. Gao
.
H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses.
IEEE Trans. Fuzzy Syst.
,
2 ,
440 -
450
-
33)
-
20. Li, H., Jing, X., Karimi, H.R.: ‘Output-feedback based H∞ control for active suspension systems with control delay’, IEEE Trans. Ind. Electron., 2014, 61, (1), pp. 436–446 (doi: 10.1109/TIE.2013.2242418).
-
34)
-
15. Lin, H., Zhai, G., Antsaklis, P.J.: ‘Robust stability and disturbance attenuation analysis of a class of networked control systems’. Proc. 42nd IEEE Conf. Decision and Control, 2003, vol. 2, pp. 1182–1187.
-
35)
-
13. Zhou, Q., Shi, P., Liu, H.H., et al: ‘Neural-network-based decentralized adaptive output- feedback control for large-scale stochastic nonlinear systems’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2012, 42, (6), pp. 1608–1609 (doi: 10.1109/TSMCB.2012.2196432).
-
36)
-
D. Yue ,
Q.-L. Han ,
J. Lam
.
Network-based robust H∞ control of systems with uncertainty.
Automatica
,
6 ,
999 -
1007
-
37)
-
L. Wu ,
X. Yao ,
W. Zheng
.
Generalized H2 fault detection for two-dimensional Markovian jump systems.
Automatica
,
8 ,
1741 -
1750
-
38)
-
H. Gao ,
X. Meng ,
T. Chen
.
Stabilization of networked control systems with a new delay characterization.
IEEE Trans. Autom. Control
,
9 ,
2142 -
2148
-
39)
-
10. Li, H., Sun, Z., Liu, H., Sun, F.: ‘Stabilisation of networked control systems using delay-dependent control gains’, IET Control Theory Appl., 2012, 6, (5), pp. 698–706 (doi: 10.1049/iet-cta.2010.0375).
-
40)
-
J. Hespanha ,
P. Naghshtabrizi ,
Y. Xu
.
A survey of recent results in networked control systems.
Proc. IEEE
,
1 ,
138 -
162
-
41)
-
H.J. Gao ,
Y. Zhao ,
T.W. Chen
.
H∞ fuzzy control of nonlinear systems under unreliable communication links.
IEEE Trans. Fuzzy Syst.
,
2 ,
265 -
278
-
42)
-
W. Zhang ,
M.S. Branicky ,
S.M. Phillips
.
Stability of networked control systems.
IEEE Control Syst. Mag.
,
84 -
99
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