Skip to main content
Erschienen in:

11.12.2023

Annular Finite-Time \(H_{\infty }\) Filtering for Mean-Field Stochastic Systems

verfasst von: Jijing Zhuang, Yan Li, Xikui Liu

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 4/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This article presents an annular finite-time \(H_{\infty }\) filtering approach for continuous-time mean-field stochastic systems (MFSSs). Our attention is focused on obtaining a set of stability criteria for analyzing the \(H_{\infty }\) performance and the annular finite-time boundedness of the filtering error system. Sufficient conditions in the form of linear matrix inequality (LMI) are established to guarantee the existence of the designed filter. Then, the filter gains are derived through a convex optimization problem. Through a simulation example, the validity of the obtained results is demonstrated.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

ATZelektronik

Die Fachzeitschrift ATZelektronik bietet für Entwickler und Entscheider in der Automobil- und Zulieferindustrie qualitativ hochwertige und fundierte Informationen aus dem gesamten Spektrum der Pkw- und Nutzfahrzeug-Elektronik. 

Lassen Sie sich jetzt unverbindlich 2 kostenlose Ausgabe zusenden.

ATZelectronics worldwide

ATZlectronics worldwide is up-to-speed on new trends and developments in automotive electronics on a scientific level with a high depth of information. 

Order your 30-days-trial for free and without any commitment.

Weitere Produktempfehlungen anzeigen
Literatur
1.
Zurück zum Zitat F. Amato, M. Ariola, C. Cosentino, Finite-time stability of linear time-varying systems: analysis and controller design. IEEE Trans. Autom. Control 55(4), 1003–1008 (2010)MathSciNetCrossRef F. Amato, M. Ariola, C. Cosentino, Finite-time stability of linear time-varying systems: analysis and controller design. IEEE Trans. Autom. Control 55(4), 1003–1008 (2010)MathSciNetCrossRef
2.
Zurück zum Zitat F. Amato, M. Carbone, M. Ariola, C. Cosentino, Finite-time stability of discrete-time systems. In Proc. Amer. Control Conf. 2, 1440–1444 (2004) F. Amato, M. Carbone, M. Ariola, C. Cosentino, Finite-time stability of discrete-time systems. In Proc. Amer. Control Conf. 2, 1440–1444 (2004)
3.
Zurück zum Zitat S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRef S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRef
4.
Zurück zum Zitat G. Cheng, H. Liu, Asynchronous finite-time \(H_{\infty }\) filtering for linear neutral semi-Markovian jumping systems under hybrid cyber attacks. J. Franklin Inst. 360(3), 1495–1522 (2023)MathSciNetCrossRef G. Cheng, H. Liu, Asynchronous finite-time \(H_{\infty }\) filtering for linear neutral semi-Markovian jumping systems under hybrid cyber attacks. J. Franklin Inst. 360(3), 1495–1522 (2023)MathSciNetCrossRef
5.
Zurück zum Zitat J. Cheng, H. Zhu, S. Zhong, Y. Zhang, Y. Zeng, Finite-time stabilization of \(H_{\infty }\) filtering for switched stochastic systems. Circuits Syst. Signal Process. 32(4), 1595–1613 (2013)MathSciNetCrossRef J. Cheng, H. Zhu, S. Zhong, Y. Zhang, Y. Zeng, Finite-time stabilization of \(H_{\infty }\) filtering for switched stochastic systems. Circuits Syst. Signal Process. 32(4), 1595–1613 (2013)MathSciNetCrossRef
6.
Zurück zum Zitat J. Cheng, H. Zhu, S. Zhong, Y. Zhang, Y. Zeng, Finite-time stabilization of \(H_{\infty }\) filtering for switched stochastic systems. Circuits Syst. Signal Process. 32(4), 1595–1613 (2013)MathSciNetCrossRef J. Cheng, H. Zhu, S. Zhong, Y. Zhang, Y. Zeng, Finite-time stabilization of \(H_{\infty }\) filtering for switched stochastic systems. Circuits Syst. Signal Process. 32(4), 1595–1613 (2013)MathSciNetCrossRef
7.
Zurück zum Zitat P. Dorato, Short-time stability in linear time-varying systems. Proc. IRE Int. Convention Record Part 4, 83–87 (1961) P. Dorato, Short-time stability in linear time-varying systems. Proc. IRE Int. Convention Record Part 4, 83–87 (1961)
8.
Zurück zum Zitat R.K. Fakher Alfahed, A.S. Al-Asadi, H.A. Badran, K.I. Ajeel, Structural, morphological, and Z-scan technique for a temperature-controllable chemical reaction synthesis of zinc sulfide nanoparticles. Appl. Phys. B 125(3), 1–11 (2019)CrossRefADS R.K. Fakher Alfahed, A.S. Al-Asadi, H.A. Badran, K.I. Ajeel, Structural, morphological, and Z-scan technique for a temperature-controllable chemical reaction synthesis of zinc sulfide nanoparticles. Appl. Phys. B 125(3), 1–11 (2019)CrossRefADS
9.
Zurück zum Zitat H. Gao, K. Shi, H. Zhang, Event-triggered finite-time \(H_{\infty }\) filtering for a class of switched nonlinear systems via the T-S fuzzy model. Circuits Syst. Signal Process. 40(7), 3161–3178 (2021)CrossRef H. Gao, K. Shi, H. Zhang, Event-triggered finite-time \(H_{\infty }\) filtering for a class of switched nonlinear systems via the T-S fuzzy model. Circuits Syst. Signal Process. 40(7), 3161–3178 (2021)CrossRef
10.
Zurück zum Zitat L. Gao, F. Luo, Z. Yan, Finite-time annular domain stability of impulsive switched systems: mode-dependent parameter approach. Int. J. Control 92(6), 1381–1392 (2019)MathSciNetCrossRef L. Gao, F. Luo, Z. Yan, Finite-time annular domain stability of impulsive switched systems: mode-dependent parameter approach. Int. J. Control 92(6), 1381–1392 (2019)MathSciNetCrossRef
11.
Zurück zum Zitat M. Gao, J. Zhao, W. Sun, Stochastic \(H_2/H_{\infty }\) control for discrete-time mean-field systems with Poisson jump. J. Franklin Inst. 358(6), 2933–2947 (2021)MathSciNetCrossRef M. Gao, J. Zhao, W. Sun, Stochastic \(H_2/H_{\infty }\) control for discrete-time mean-field systems with Poisson jump. J. Franklin Inst. 358(6), 2933–2947 (2021)MathSciNetCrossRef
12.
Zurück zum Zitat J. Jiao, H.L. Trentelman, M.K. Camlibel, \(H_2\) and \(H_{\infty }\) suboptimal distributed filters design for linear systems. IEEE Trans. Autom. Control 68, 2560–2567 (2023)CrossRef J. Jiao, H.L. Trentelman, M.K. Camlibel, \(H_2\) and \(H_{\infty }\) suboptimal distributed filters design for linear systems. IEEE Trans. Autom. Control 68, 2560–2567 (2023)CrossRef
13.
Zurück zum Zitat B.P. Kellerhals, Financial Pricing Models in Continuous Time and Kalman Filtering (Springer-Verlag, Berlin, 2001)CrossRef B.P. Kellerhals, Financial Pricing Models in Continuous Time and Kalman Filtering (Springer-Verlag, Berlin, 2001)CrossRef
14.
Zurück zum Zitat Y. Lin, T. Zhang, W. Zhang, Pareto-based guaranteed cost control of the uncertain mean-field stochastic systems in infinite horizon. Automatica 92, 197–209 (2018)MathSciNetCrossRef Y. Lin, T. Zhang, W. Zhang, Pareto-based guaranteed cost control of the uncertain mean-field stochastic systems in infinite horizon. Automatica 92, 197–209 (2018)MathSciNetCrossRef
15.
Zurück zum Zitat R. Liu, Y. Li, X. Liu, Linear-quadratic optimal control for unknown mean-field stochastic discrete-time system via adaptive dynamic programming approach. Neurocomputing 282, 16–24 (2018)CrossRef R. Liu, Y. Li, X. Liu, Linear-quadratic optimal control for unknown mean-field stochastic discrete-time system via adaptive dynamic programming approach. Neurocomputing 282, 16–24 (2018)CrossRef
16.
Zurück zum Zitat X. Liu, Q. Liu, Y. Li, Finite-time guaranteed cost control for uncertain mean-field stochastic systems. J. Franklin Inst. 357(5), 2813–2829 (2020)MathSciNetCrossRef X. Liu, Q. Liu, Y. Li, Finite-time guaranteed cost control for uncertain mean-field stochastic systems. J. Franklin Inst. 357(5), 2813–2829 (2020)MathSciNetCrossRef
17.
Zurück zum Zitat H. Lu, Y. Xu, X. Song, W. Zhou, Adaptive event-triggered \(H_{\infty }\) state estimation of semi-Markovian jump neural networks with randomly occurred sensor nonlinearity. Int. J. Robust Nonlin. 32(12), 6623–6646 (2022)MathSciNetCrossRef H. Lu, Y. Xu, X. Song, W. Zhou, Adaptive event-triggered \(H_{\infty }\) state estimation of semi-Markovian jump neural networks with randomly occurred sensor nonlinearity. Int. J. Robust Nonlin. 32(12), 6623–6646 (2022)MathSciNetCrossRef
18.
Zurück zum Zitat L. Ma, T. Zhang, W. Zhang, \(H_{\infty }\) control for continuous-time mean-field stochastic systems. Asian J. Control 18(5), 1630–1640 (2016)MathSciNetCrossRef L. Ma, T. Zhang, W. Zhang, \(H_{\infty }\) control for continuous-time mean-field stochastic systems. Asian J. Control 18(5), 1630–1640 (2016)MathSciNetCrossRef
19.
Zurück zum Zitat X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Switching (Imperial College Press, London, 2006)CrossRef X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Switching (Imperial College Press, London, 2006)CrossRef
20.
Zurück zum Zitat J. Moon, T. Başar, Linear quadratic mean-field Stackelberg differential games. Automatica 97(3), 200–213 (2018)MathSciNetCrossRef J. Moon, T. Başar, Linear quadratic mean-field Stackelberg differential games. Automatica 97(3), 200–213 (2018)MathSciNetCrossRef
21.
Zurück zum Zitat J. Qian, P. Duan, Z. Duan, L. Shi, Event-triggered distributed state estimation: a conditional expectation method. IEEE Trans. Autom. Control 68, 6361–6368 (2023)MathSciNetCrossRef J. Qian, P. Duan, Z. Duan, L. Shi, Event-triggered distributed state estimation: a conditional expectation method. IEEE Trans. Autom. Control 68, 6361–6368 (2023)MathSciNetCrossRef
22.
Zurück zum Zitat S. Sun, T. Li, Y. Pang, X. Hua, Multiple delay-dependent event-triggered finite-time \(H_{\infty }\) filtering for uncertain networked random systems against state and input constraints. Appl. Math. Comput 415, 126711 (2022) S. Sun, T. Li, Y. Pang, X. Hua, Multiple delay-dependent event-triggered finite-time \(H_{\infty }\) filtering for uncertain networked random systems against state and input constraints. Appl. Math. Comput 415, 126711 (2022)
23.
Zurück zum Zitat X. Sun, D. Yang, G. Zong, Annular finite-time \(H_{\infty }\) control of switched fuzzy systems: a switching dynamic event-triggered control approach. Nonlinear Anal. Hybrid. 41, 101050 (2021)MathSciNetCrossRef X. Sun, D. Yang, G. Zong, Annular finite-time \(H_{\infty }\) control of switched fuzzy systems: a switching dynamic event-triggered control approach. Nonlinear Anal. Hybrid. 41, 101050 (2021)MathSciNetCrossRef
24.
Zurück zum Zitat G. Tartaglione, M. Ariola, C. Cosentino, G. De Tommasi, A. Pironti, F. Amato, Annular finite-time stability analysis and synthesis of stochastic linear time-varying systems. Int. J. Control 94(8), 2252–2263 (2021)MathSciNetCrossRef G. Tartaglione, M. Ariola, C. Cosentino, G. De Tommasi, A. Pironti, F. Amato, Annular finite-time stability analysis and synthesis of stochastic linear time-varying systems. Int. J. Control 94(8), 2252–2263 (2021)MathSciNetCrossRef
25.
Zurück zum Zitat J. Wang, S. Ma, C. Zhang, Finite-time \(H_{\infty }\) filtering for nonlinear continuous-time singular semi-markov jump systems. Asian J. Control 21(2), 1017–1027 (2019)MathSciNetCrossRef J. Wang, S. Ma, C. Zhang, Finite-time \(H_{\infty }\) filtering for nonlinear continuous-time singular semi-markov jump systems. Asian J. Control 21(2), 1017–1027 (2019)MathSciNetCrossRef
26.
Zurück zum Zitat J. Wang, S. Ma, C. Zhang, M. Fu, Finite-time \(H_{\infty }\) filtering for nonlinear singular systems with nonhomogeneous Markov jumps. IEEE Trans. Cybern. 49(6), 2133–2143 (2018)PubMedCrossRef J. Wang, S. Ma, C. Zhang, M. Fu, Finite-time \(H_{\infty }\) filtering for nonlinear singular systems with nonhomogeneous Markov jumps. IEEE Trans. Cybern. 49(6), 2133–2143 (2018)PubMedCrossRef
27.
Zurück zum Zitat X.L. Wang, G.H. Yang, \(H_{\infty }\) filtering for T-S fuzzy systems with multiple time-varying delays: an improved delays-dependent region partitioning method. Inf. Sci. 481, 368–380 (2019)MathSciNetCrossRef X.L. Wang, G.H. Yang, \(H_{\infty }\) filtering for T-S fuzzy systems with multiple time-varying delays: an improved delays-dependent region partitioning method. Inf. Sci. 481, 368–380 (2019)MathSciNetCrossRef
28.
Zurück zum Zitat Z. Wang, Y. Liu, X. Liu, \(H_{\infty }\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. Automatica 44(5), 1268–1277 (2008)MathSciNetCrossRef Z. Wang, Y. Liu, X. Liu, \(H_{\infty }\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. Automatica 44(5), 1268–1277 (2008)MathSciNetCrossRef
29.
Zurück zum Zitat C.F. Wu, B.S. Chen, W. Zhang, Multiobjective \(H_ {2}/H_ {\infty }\) control design of the nonlinear mean-field stochastic jump-diffusion systems via fuzzy approach. IEEE Trans. Fuzzy Syst. 27(4), 686–700 (2018)CrossRef C.F. Wu, B.S. Chen, W. Zhang, Multiobjective \(H_ {2}/H_ {\infty }\) control design of the nonlinear mean-field stochastic jump-diffusion systems via fuzzy approach. IEEE Trans. Fuzzy Syst. 27(4), 686–700 (2018)CrossRef
30.
Zurück zum Zitat L. Xu, Y. Mo, L. Xie, Remote state estimation with stochastic event-triggered sensor schedule and packet drops. IEEE Trans. Autom. Control 65, 4981–4988 (2020)MathSciNetCrossRef L. Xu, Y. Mo, L. Xie, Remote state estimation with stochastic event-triggered sensor schedule and packet drops. IEEE Trans. Autom. Control 65, 4981–4988 (2020)MathSciNetCrossRef
31.
Zurück zum Zitat N. Xu, L. Sun, An improved \(H_{\infty }\) filtering for Markovian jump system with time-varying delay based on finite frequency. J. Franklin Inst. 356(12), 6724–6740 (2019)MathSciNetCrossRef N. Xu, L. Sun, An improved \(H_{\infty }\) filtering for Markovian jump system with time-varying delay based on finite frequency. J. Franklin Inst. 356(12), 6724–6740 (2019)MathSciNetCrossRef
32.
Zurück zum Zitat J. Yan, X. Yang, Y. Mo, K. Yo, A distributed implementation of steady-state Kalman filter. IEEE Trans. Autom. Control 68, 2490–2497 (2023)MathSciNetCrossRef J. Yan, X. Yang, Y. Mo, K. Yo, A distributed implementation of steady-state Kalman filter. IEEE Trans. Autom. Control 68, 2490–2497 (2023)MathSciNetCrossRef
33.
Zurück zum Zitat Z. Yan, T. Yang, B. Zhu, G. Chang, Finite-time annular domain stability and stabilisation of linear positive systems. Int. J Control (2022) Z. Yan, T. Yang, B. Zhu, G. Chang, Finite-time annular domain stability and stabilisation of linear positive systems. Int. J Control (2022)
34.
Zurück zum Zitat Z. Yan, G. Zhang, J. Wang, Finite-time stability and stabilization of linear stochastic systems. In Proc. \(29\)th Chin. Control Conf., pages 1115–1120 (2010) Z. Yan, G. Zhang, J. Wang, Finite-time stability and stabilization of linear stochastic systems. In Proc. \(29\)th Chin. Control Conf., pages 1115–1120 (2010)
35.
Zurück zum Zitat Z. Yan, M. Zhang, G. Chang, H. Lv, J.H. Park, Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach. Appl. Math. Comput. 412, 126589 (2022) Z. Yan, M. Zhang, G. Chang, H. Lv, J.H. Park, Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach. Appl. Math. Comput. 412, 126589 (2022)
36.
Zurück zum Zitat Z. Yan, W. Zhang, G. Zhang, Finite-time stability and stabilization of Itô stochastic systems with Markovian switching: mode-dependent parameter approach. IEEE Trans. Autom. Control 60(9), 2428–2433 (2015)CrossRef Z. Yan, W. Zhang, G. Zhang, Finite-time stability and stabilization of Itô stochastic systems with Markovian switching: mode-dependent parameter approach. IEEE Trans. Autom. Control 60(9), 2428–2433 (2015)CrossRef
37.
Zurück zum Zitat Z. Yan, X. Zhou, G. Chang, Z. Gao, Finite-time annular domain stability and stabilization of stochastic systems with semi-Markovian switching. IEEE Trans. Autom. Control 68(10), 6247–6254 (2023)MathSciNetCrossRef Z. Yan, X. Zhou, G. Chang, Z. Gao, Finite-time annular domain stability and stabilization of stochastic systems with semi-Markovian switching. IEEE Trans. Autom. Control 68(10), 6247–6254 (2023)MathSciNetCrossRef
38.
Zurück zum Zitat X. Yi, G. Li, Y. Liu, F. Fang, Event-triggered \(H_{\infty }\) filtering for nonlinear networked control systems via T-S fuzzy model approach. Neurocomputing 448, 344–352 (2021)CrossRef X. Yi, G. Li, Y. Liu, F. Fang, Event-triggered \(H_{\infty }\) filtering for nonlinear networked control systems via T-S fuzzy model approach. Neurocomputing 448, 344–352 (2021)CrossRef
39.
Zurück zum Zitat J. Yin, S. Khoo, Z. Man, X. Yu, Finite-time stability and instability of stochastic nonlinear systems. Automatica 47(12), 2671–2677 (2011)MathSciNetCrossRef J. Yin, S. Khoo, Z. Man, X. Yu, Finite-time stability and instability of stochastic nonlinear systems. Automatica 47(12), 2671–2677 (2011)MathSciNetCrossRef
40.
Zurück zum Zitat H. Zhang, Q. Qi, M. Fu, Optimal stabilization control for discrete-time mean-field stochastic systems. IEEE Trans. Autom. Control 64(3), 1125–1136 (2018)MathSciNetCrossRef H. Zhang, Q. Qi, M. Fu, Optimal stabilization control for discrete-time mean-field stochastic systems. IEEE Trans. Autom. Control 64(3), 1125–1136 (2018)MathSciNetCrossRef
41.
Zurück zum Zitat T. Zhang, F. Deng, W. Zhang, Robust \(H_{\infty }\) filtering for nonlinear discrete-time stochastic systems. Automatica 123, 109343 (2021)MathSciNetCrossRef T. Zhang, F. Deng, W. Zhang, Robust \(H_{\infty }\) filtering for nonlinear discrete-time stochastic systems. Automatica 123, 109343 (2021)MathSciNetCrossRef
42.
Zurück zum Zitat Y. Zhang, C. Liu, Y. Song, Finite-time \(H_{\infty }\) filtering for discrete-time Markovian jump systems. J. Franklin Inst. 350(6), 1579–1595 (2013)MathSciNetCrossRef Y. Zhang, C. Liu, Y. Song, Finite-time \(H_{\infty }\) filtering for discrete-time Markovian jump systems. J. Franklin Inst. 350(6), 1579–1595 (2013)MathSciNetCrossRef
43.
Zurück zum Zitat X. Zheng, H. Zhang, Z. Wang, C. Zhang, H. Yan, Finite-time dynamic event-triggered distributed \(H_{\infty }\) filtering for T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 30(7), 2476–2486 (2021)CrossRef X. Zheng, H. Zhang, Z. Wang, C. Zhang, H. Yan, Finite-time dynamic event-triggered distributed \(H_{\infty }\) filtering for T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 30(7), 2476–2486 (2021)CrossRef
44.
Zurück zum Zitat J. Zhuang, X. Liu, Y. Li, Event-triggered annular finite-time \(H_{\infty }\) filtering for stochastic network systems. J. Franklin Inst. 359(18), 11208–11228 (2022)MathSciNetCrossRef J. Zhuang, X. Liu, Y. Li, Event-triggered annular finite-time \(H_{\infty }\) filtering for stochastic network systems. J. Franklin Inst. 359(18), 11208–11228 (2022)MathSciNetCrossRef
45.
Zurück zum Zitat G. Zong, H. Ren, H.R. Karimi, Event-triggered communication and annular finite-time \(H_{\infty }\) filtering for networked switched systems. IEEE Trans. Cybern. 51(1), 309–317 (2020)PubMedCrossRef G. Zong, H. Ren, H.R. Karimi, Event-triggered communication and annular finite-time \(H_{\infty }\) filtering for networked switched systems. IEEE Trans. Cybern. 51(1), 309–317 (2020)PubMedCrossRef
Metadaten
Titel
Annular Finite-Time Filtering for Mean-Field Stochastic Systems
verfasst von
Jijing Zhuang
Yan Li
Xikui Liu
Publikationsdatum
11.12.2023
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 4/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-023-02568-z