## Optimal $$\mathcal H_{\infty}$$ filtering in networked control systems with multiple packet dropouts.(English)Zbl 1153.93034

Summary: This paper studies the problem of $$\mathcal H_{\infty}$$ filtering in Networked Control Systems (NCSs) with multiple packet dropouts. A new formulation enables us to assign separate dropout rates from the sensors to the controller and from the controller to the actuators. By employing the new formulation, random dropout rates are transformed into stochastic parameters in the system’s representation. A generalized $$\mathcal H_{\infty}$$-norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived. The stochastic $$\mathcal H_{\infty}$$-norm of the filtering error is used as a criterion for filter design in the NCS framework. A set of linear matrix inequalities is given to solve the corresponding filter design problem. A simulation example supports the theory.

### MSC:

 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory
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### References:

 [1] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 [2] Chen, T.; Francis, B.A., Optimal sampled-data control systems, (1995), Springer New-York · Zbl 0847.93040 [3] de Souza, C.E.; Xie, L., On the discrete-time bounded real lemma with application in the characterization of static state feedback $$\mathcal{H}_\infty$$ controllers, Systems control lett., 18, 61-71, (1992) · Zbl 0743.93038 [4] El Bouhtouri, A.; Hinrichsen, D.; Pritchard, A.J., $$\mathcal{H}_\infty$$-type control for discrete-time stochastic systems, Int. J. robust nonlinear control, 9, 923-948, (1999) · Zbl 0934.93022 [5] Furuta, K.; Phoojaruenchanachai, S., An algebraic approach to discrete-time $$\mathcal{H}_\infty$$ control problems, (), 3067-3072 [6] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to $$\mathcal{H}_\infty$$ control, Int. J. robust nonlinear control, 4, 4, 421-448, (1994) · Zbl 0808.93024 [7] Geromel, J.C.; Bernussou, J.; Garcia, G.; de Oliveria, M.C., $$\mathcal{H}_2$$ and $$\mathcal{H}_\infty$$ robust filtering for discrete-time linear systems, SIAM J. control optim., 38, 5, 1353-1368, (2000) · Zbl 0958.93091 [8] Hespanha, J.P.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems, Proc. IEEE, 95, 1, 138-162, (2007) [9] H. Li, Z. Sun, F. Wu, F. Sun, Optimal controller design for a class of networked control systems, in: Proc. 5th International Conference on Hybrid Intelligent Systems, 2005 [10] Ling, Q.; Lemmon, M.D., Power spectral analysis of networked control systems with data dropouts, IEEE trans. automat. control, 49, 6, 955-960, (2004) · Zbl 1365.93162 [11] Morozan, T., Stabilization of some stochastic discrete-time control systems, Stoch. anal. appl., 1, 1, 89-116, (1983) · Zbl 0517.93061 [12] J. Nilson, Analysis and design of real-time systems with random delays, Lic Tech Thesis, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1996 [13] Palhares, R.M.; Peres, P.L.D., Optimal filtering schemes for linear discrete-time systems: A linear matrix inequality approach, Int. J. systems sci., 29, 6, 587-593, (1998) [14] Sahebsara, M.; Chen, T.; Shah, S.L., Optimal $$\mathcal{H}_2$$ filtering with random sensor delay, multiple packet dropout and uncertain observations, Internat. J. control, 80, 2, 292-301, (2007) · Zbl 1140.93486 [15] Sahebsara, M.; Chen, T.; Shah, S.L., Optimal $$\mathcal{H}_2$$ filtering in networked control systems with multiple packet dropout, IEEE trans. automat. control, 52, 8, 1508-1513, (2007) · Zbl 1366.93659 [16] Touri, R.; Hadjicostis, CN., Stabilisation with feedback control utilising packet-dropping network links, IET control theory appl., 1, 1, 334-342, (2007) [17] Yu, J.; Yu, S.; Wang, H., Survey on the performance analysis of networked control systems, (), 5068-5073 [18] Yang, F.; Wang, Z.; Hung, Y.S.; Gani, M., $$\mathcal{H}_\infty$$ control for networked systems with random communication delays, IEEE trans. automat. control, 51, 3, 511-518, (2006) · Zbl 1366.93167 [19] Yang, T.C., Networked control system: A brief survey, IEE proc. control theory appl., 153, 4, 403-412, (2006) [20] M. Yu, L. Wang, G. Xie, T. Chu, Stabilization of NCS with data packet dropout via switched system approach, in: Proc. IEEE International Symposium on Computer Aided Control Systems Design, 2004, pp. 362-367 [21] Yue, D.; Han, Q.L.; Peng, C., State feedback controller design of networked control systems, IEEE trans. circuits syst. II-express briefs, 51, 11, 640-644, (2004) [22] Wang, Z.; Yang, F.; Ho, D.W.C.; Liu, X., Robust $$\mathcal{H}_\infty$$ filtering for stochastic time-delay systems with missing measurements, IEEE trans. signal processing, 54, 7, 2579-2587, (2006) · Zbl 1373.94729
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