×

Event-based state and unknown input estimation for uncertain systems with stochastic nonlinearities. (English) Zbl 1483.93421

Summary: In this paper, the event-based state and unknown input estimation (SUIE) problem is investigated for a class of stochastic systems subject to parameter uncertainties and stochastic nonlinearities. For the purpose of reducing the energy consumption in data transmission, an event-triggering protocol is employed to regulate whether the current measurement is transmitted by the sensor. Utilising the event-triggered measurement, a recursive estimator is constructed to concurrently estimate the state and the unknown input. The upper bounds of estimation error covariances are given explicitly for both the state and the unknown input estimates. By means of the completing-the-square technique and Lagrange multiplier method, the estimator gain matrices are designed which minimise the obtained upper bounds. Finally, a numerical example is given to show the effectiveness of the proposed SUIE method.

MSC:

93C65 Discrete event control/observation systems
93E10 Estimation and detection in stochastic control theory
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information
Full Text: DOI

References:

[1] Achour, H.; Boukhetala, D.; Labdelaoui, H., An observer-based robust \(####\) controller design for uncertain Takagi-Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation, International Journal of Systems Science, 51, 14, 2563-2581 (2020) · Zbl 1483.93123 · doi:10.1080/00207721.2020.1797922
[2] Arasaratnam, I.; Haykin, S., Cubature Kalman filters, IEEE Transansactions on Automatic Control, 54, 6, 1254-1269 (2009) · Zbl 1367.93637 · doi:10.1109/TAC.2009.2019800
[3] Chen, W.; Ding, D.; Ge, X.; Han, Q.; Wei, G., \(####\) containment control of multi-agent systems under event-triggered communication scheduling: The finite-horizon case, IEEE Transansactions on Cybernetics, 50, 4, 1372-1382 (2020) · doi:10.1109/TCYB.6221036
[4] Ding, D.; Han, Q.; Wang, Z.; Ge, X., A survey on model-based distributed control and filtering for industrial cyber-physical systems, IEEE Transactions on Industrial Informatics, 15, 5, 2483-2499 (2019) · doi:10.1109/TII.9424
[5] Ding, D.; Wang, Z.; Han, Q., A set-membership approach to event-triggered filtering for general nonlinear systems over sensor networks, IEEE Transactions on Automatic Control, 65, 4, 1792-1799 (2020) · Zbl 1533.93453 · doi:10.1109/TAC.9
[6] Fang, H.; Shi, Y.; Yi, J., On stable simultaneous input and state estimation for discrete-time linear, International Journal of Adaptive Control and Signal Processing, 25, 8, 671-686 (2011) · Zbl 1227.93112 · doi:10.1002/acs.v25.8
[7] Fesharaki, S. J.; Sheikholeslam, F.; Kamali, M.; Talebi, A., Tractable robust model predictive control with adaptive sliding mode for uncertain nonlinear systems, International Journal of Systems Science, 51, 12, 2204-2216 (2020) · Zbl 1483.93147 · doi:10.1080/00207721.2020.1793230
[8] Friedland, B., Treatment of bias in recursive filtering, IEEE Transactions on Automatic Control, 14, 4, 359-367 (1969) · doi:10.1109/TAC.1969.1099223
[9] Gao, M.; Zhang, W.; Sheng, L.; Zhou, D., Distributed fault estimation for delayed complex networks with Round-Robin protocol based on unknown input observer, Journal of the Franklin Institute, 357, 13, 8678-8702 (2020) · Zbl 1448.93118 · doi:10.1016/j.jfranklin.2020.04.012
[10] Ge, X.; Han, Q.; Wang, Z., A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks, IEEE Transactions on Cybernetics, 49, 1, 171-183 (2017) · doi:10.1109/TCYB.2017.2769722
[11] Ge, X.; Han, Q.; Zhang, X.; Ding, L.; Yang, F., Distributed event-triggered estimation over sensor networks: A survey, IEEE Transactions on Cybernetics, 50, 3, 1306-1320 (2019) · doi:10.1109/TCYB.6221036
[12] Gillijns, S.; De Moor, B., Unbiased minimum-variance input and state estimation for linear discrete-time systems, Automatica, 43, 1, 111-116 (2007) · Zbl 1140.93480 · doi:10.1016/j.automatica.2006.08.002
[13] Gillijns, S.; De Moor, B., Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough, Automatica, 43, 5, 934-937 (2007) · Zbl 1117.93366 · doi:10.1016/j.automatica.2006.11.016
[14] Hsieh, C. S., Robust two-stage Kalman filters for systems with unknown inputs, IEEE Transactions on Automatic Control, 45, 12, 2374-2378 (2000) · Zbl 0990.93130 · doi:10.1109/9.895577
[15] Hsieh, C. S., Unbiased minimum-variance input and state estimation for systems with unknown inputs: A system reformation approach, Automatica, 84, 236-240 (2017) · Zbl 1376.93101 · doi:10.1016/j.automatica.2017.06.037
[16] Hu, J.; Wang, Z.; Gao, H.; Stergioulas, L. K., Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements, Automatica, 48, 9, 2007-2015 (2012) · Zbl 1257.93099 · doi:10.1016/j.automatica.2012.03.027
[17] Hu, L.; Wang, Z.; Han, Q.; Liu, X., Event-based input and state estimation for linear discrete time-varying systems, International Journal of Control, 91, 1, 101-113 (2018) · Zbl 1390.93758 · doi:10.1080/00207179.2016.1269205
[18] Hu, J.; Wang, Z.; Shen, B.; Gao, H., Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements, International Journal of Control, 86, 4, 650-663 (2013) · Zbl 1278.93269 · doi:10.1080/00207179.2012.756149
[19] Hu, J.; Wang, Z.; Shen, B.; Gao, H., Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays, IEEE Transactions on Signal Processing, 61, 5, 1230-1238 (2013) · Zbl 1393.94261 · doi:10.1109/TSP.2012.2232660
[20] Li, Q.; Shen, B.; Wang, Z.; Sheng, W., Recursive distributed filtering over sensor networks on Gilbert-Elliott channels: A dynamic event-triggered approach, Automatica, 113 (2020) · Zbl 1440.93253 · doi:10.1016/j.automatica.2019.108681
[21] Li, Q.; Wang, Z.; Sheng, W.; Alsaadi, F. E.; Alsaadi, F. E., Dynamic event-triggered mechanism for \(####\) non-fragile state estimation of complex networks under randomly occurring sensor saturations, Information Sciences, 509, 304-316 (2020) · Zbl 1470.93099 · doi:10.1016/j.ins.2019.08.063
[22] Lu, P.; Van Kampen, E. J.; De Visser, C. C.; Chu, Q., Framework for state and unknown input estimation of linear time-varying systems, Automatica, 73, 145-154 (2016) · Zbl 1372.93200 · doi:10.1016/j.automatica.2016.07.009
[23] Martinez-Garcia, C.; Astorga-Zaragoza, C.; Puig, V.; Reyes-Reyes, J.; Lopez-Estrada, F., A simple nonlinear observer for state and unknown input estimation: DC motor applications, IEEE Transactions on Circuits and Systems II-Express Briefs, 67, 4, 710-714 (2020) · doi:10.1109/TCSII.8920
[24] Niu, Y.; Sheng, L.; Gao, M.; Zhou, D., Dynamic event-triggered state estimation for continuous-time polynomial nonlinear systems with external disturbances, IEEE Transactions on Industrial Informatics (2020) · doi:10.1109/TII.2020.3015004
[25] Sathishkumar, M.; Liu, Y., Resilient event-triggered fault-tolerant control for networked control systems with randomly occurring nonlinearities and DoS attacks, International Journal of Systems Science, 51, 14, 2712-2732 (2020) · Zbl 1483.93404 · doi:10.1080/00207721.2020.1801880
[26] Shen, B.; Wang, Z.; Wang, D.; Liu, H., Distributed state-saturated recursive filtering over sensor networks under Round-Robin protocol, IEEE Transactions on Cybernetics, 50, 8, 3605-3615 (2020) · doi:10.1109/TCYB.6221036
[27] Shen, B.; Wang, Z.; Wang, D.; Luo, J.; Pu, H.; Peng, Y., Finite-horizon filtering for a class of nonlinear time-delayed systems with an energy harvesting sensor, Automatica, 100, 144-152 (2019) · Zbl 1411.93176 · doi:10.1016/j.automatica.2018.11.010
[28] Shu, H.; Zhang, S.; Shen, B.; Liu, Y., Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises, International Journal of General Systems, 45, 5, 648-661 (2016) · Zbl 1342.93108 · doi:10.1080/03081079.2015.1106732
[29] Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104 · doi:10.1109/TAC.2007.904277
[30] Tan, H.; Shen, B.; Liu, Y.; Alsaedi, A.; Ahmad, B., Event-triggered multi-rate fusion estimation for uncertain system with stochastic nonlinearities and colored measurement noises, Information Fusion, 36, 313-320 (2017) · doi:10.1016/j.inffus.2016.12.003
[31] Tan, H.; Shen, B.; Peng, K.; Liu, H., Robust recursive filtering for uncertain stochastic systems with amplify-and-forward relays, International Journal of Systems Science, 51, 7, 1188-1199 (2020) · Zbl 1483.93664 · doi:10.1080/00207721.2020.1754960
[32] Theodor, Y.; Shaked, U., Robust discrete-time minimum-variance filtering, IEEE Transactions on Signal Processing, 44, 2, 181-189 (1996) · doi:10.1109/78.485915
[33] Wang, L.; Wang, Z.; Han, Q.; Wei, G., Event-based variance-constrained \(####\) filtering for stochastic parameter systems over sensor networks with successive missing measurements, IEEE Transactions on Cybernetics, 48, 3, 1007-1017 (2018) · doi:10.1109/TCYB.2017.2671032
[34] Wang, F.; Wang, Z.; Liang, J.; Liu, X., Event-triggered recursive filtering for shift-varying linear repetitive processes, IEEE Transactions on Cybernetics, 50, 4, 1761-1770 (2020) · doi:10.1109/TCYB.6221036
[35] Wang, Y.; Zhao, D.; Li, Y.; Ding, S. X., Unbiased minimum variance fault and state estimation for linear discrete time-varying two-dimensional systems, IEEE Transactions on Automatic Control, 62, 10, 5463-5469 (2017) · Zbl 1390.93773 · doi:10.1109/TAC.2017.2697210
[36] Wei, G.; Liu, L.; Wang, L.; Ding, D., Event-triggered control for discrete-time systems with unknown nonlinearities: An interval observer-based approach, International Journal of Systems Science, 51, 6, 1019-1031 (2020) · Zbl 1483.93415 · doi:10.1080/00207721.2020.1746441
[37] Yang, F.; Wang, Z.; Feng, G.; Liu, X., Robust filtering with randomly varying sensor delay: The finite-horizon case, IEEE Transactions on Circuits and Systems, Part I: Regular Papers, 56, 3, 664-672 (2009) · Zbl 1468.94274 · doi:10.1109/TCSI.2008.918009
[38] Yang, F.; Wang, Z.; Huang, Y., Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises, IEEE Transansactions on Automatic Control, 47, 7, 1179-1183 (2002) · Zbl 1364.93817 · doi:10.1109/TAC.2002.800668
[39] Yong, S. Z.; Zhu, M.; Frazzoli, E., A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems, Automatica, 63, 321-329 (2016) · Zbl 1329.93148 · doi:10.1016/j.automatica.2015.10.040
[40] Yong, S. Z.; Zhu, M.; Frazzoli, E., Simultaneous input and state estimation for linear time-varying continuous-time stochastic systems, IEEE Transactions on Automatic Control, 62, 5, 2531-2538 (2017) · Zbl 1366.93663 · doi:10.1109/TAC.2016.2601688
[41] Zhang, X.; Han, Q.; Ge, X.; Ding, D.; Ding, L.; Yue, D.; Peng, C., Networked control systems: A survey of trends and techniques, IEEE/CAA Journal of Automatica Sinica, 7, 1, 1-7 (2020) · doi:10.1109/JAS.6570654
[42] Zhou, X.; Chen, Y.; Wang, Q.; Zhang, K.; Xue, A., Event-triggered finite-time \(####\) control of networked state-saturated switched systems, International Journal of Systems Science, 51, 10, 1744-1758 (2020) · Zbl 1485.93374 · doi:10.1080/00207721.2020.1777344
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.