A sampled-data approach to distributed H∞ resilient state estimation for a class of nonlinear time-delay systems over sensor networks

Abstract This paper deals with the distributed sampled-data H ∞ state estimation problem for a class of continuous-time nonlinear systems with infinite-distributed delays. To cater for possible implementation errors, the estimator gain is allowed to have certain bounded parameter variations. A sensor network is deployed to acquire the plant output by collaborating with their neighbors according to a given network topology. The individually sampled sensor measurement is transmitted to the corresponding estimator through a digital communication channel. By utilizing the input delay approach, the effect of the sampling intervals is transformed into an equivalent bounded time-varying delay. A set of sampled-data distributed estimators is designed for the addressed nonlinear systems in order to meet the following three performance requirements: (1) the asymptotic convergence of the estimation error dynamics; (2) the H ∞ disturbance attenuation/rejection behavior against the exogenous disturbances; and (3) the resilience against possible gain variations. A Lyapunov functional approach is put forward to obtain the existence conditions for the desired estimators which are then parameterized in light of the feasibility of some matrix inequalities. An illustrative numerical example is given to demonstrate the usefulness of the proposed estimator design algorithm.

[1]  Jinde Cao,et al.  A New Framework for Analysis on Stability and Bifurcation in a Class of Neural Networks With Discrete and Distributed Delays , 2015, IEEE Transactions on Cybernetics.

[2]  Gang Feng,et al.  Multi-rate distributed fusion estimation for sensor networks with packet losses , 2012, Autom..

[3]  Zidong Wang,et al.  Event-triggered distributed ℋ ∞ state estimation with packet dropouts through sensor networks , 2015 .

[4]  Abraham O. Fapojuwo,et al.  A Survey of System Architecture Requirements for Health Care-Based Wireless Sensor Networks , 2011, Sensors.

[5]  Yonggui Kao,et al.  A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems , 2015, Autom..

[6]  Qing-Long Han,et al.  Distributed sampled-data asynchronous H∞ filtering of Markovian jump linear systems over sensor networks , 2016, Signal Process..

[7]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

[8]  Qing-Long Han,et al.  A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs , 2016, IEEE Transactions on Cybernetics.

[9]  Alexander G. Loukianov,et al.  Optimal Filtering for Polynomial Systems over Switching Delayed Observations , 2013, 2013 American Control Conference.

[10]  Qing-Long Han,et al.  Event-based H∞ filtering for sampled-data systems , 2015, Autom..

[11]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..

[12]  Ligang Wu,et al.  Nonfragile Output Tracking Control of Hypersonic Air-Breathing Vehicles With an LPV Model , 2013, IEEE/ASME Transactions on Mechatronics.

[13]  Peng Shi,et al.  Sampled-Data Exponential Synchronization of Complex Dynamical Networks With Time-Varying Coupling Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[15]  Fuad E. Alsaadi,et al.  Non-fragile state estimation for discrete Markovian jumping neural networks , 2016, Neurocomputing.

[16]  Raquel Caballero-Águila,et al.  Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements , 2015, Int. J. Gen. Syst..

[17]  Shengyuan Xu,et al.  Reachable set estimation for discrete‐time linear systems with time delays , 2015 .

[18]  Qing-Long Han,et al.  An Overview and Deep Investigation on Sampled-Data-Based Event-Triggered Control and Filtering for Networked Systems , 2017, IEEE Transactions on Industrial Informatics.

[19]  Tingwen Huang,et al.  An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities , 2016, IEEE Transactions on Cybernetics.

[20]  Francesco Chiti,et al.  Using wireless sensor networks to support intelligent transportation systems , 2010, Ad Hoc Networks.

[21]  Giorgio Battistelli,et al.  Stability of consensus extended Kalman filter for distributed state estimation , 2016, Autom..

[22]  Xiao Lu,et al.  Robust Kalman Filtering for Discrete-Time Systems With Measurement Delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Fuad E. Alsaadi,et al.  A Resilient Approach to Distributed Filter Design for Time-Varying Systems Under Stochastic Nonlinearities and Sensor Degradation , 2017, IEEE Transactions on Signal Processing.

[24]  Nan Li,et al.  Sampled-data state estimation for delayed neural networks with Markovian jumping parameters , 2013 .

[25]  Soummya Kar,et al.  Distributed Kalman Filtering : Weak Consensus Under Weak Detectability , 2011 .

[26]  Fuad E. Alsaadi,et al.  $H_\infty $ Control for 2-D Fuzzy Systems With Interval Time-Varying Delays and Missing Measurements , 2017, IEEE Transactions on Cybernetics.

[27]  Hari Om,et al.  Authentication protocol for wireless sensor networks applications like safety monitoring in coal mines , 2016, Comput. Networks.

[28]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[29]  Hak-Keung Lam,et al.  Fuzzy Sampled-Data Control for Uncertain Vehicle Suspension Systems , 2014, IEEE Transactions on Cybernetics.

[30]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[31]  Gerhard P. Hancke,et al.  Industrial Wireless Sensor Networks: Challenges, Design Principles, and Technical Approaches , 2009, IEEE Transactions on Industrial Electronics.

[32]  Derui Ding,et al.  Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks , 2017, Autom..

[33]  Xinghuo Yu,et al.  Survey on Recent Advances in Networked Control Systems , 2016, IEEE Transactions on Industrial Informatics.

[34]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[35]  Yurong Liu,et al.  Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays , 2016, Neurocomputing.

[36]  Luis Rodrigues,et al.  Stability and stabilization of linear sampled-data systems with multi-rate samplers and time driven zero order holds , 2014, Autom..

[37]  H. Karimi.  Robust H 1 Filter Design for Uncertain Linear Systems Over Network with Network-Induced Delays and Output Quantization , 2009 .

[38]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[39]  Yeung Sam Hung,et al.  Distributed $H_{\infty}$ Filtering for Polynomial Nonlinear Stochastic Systems in Sensor Networks , 2011, IEEE Transactions on Industrial Electronics.

[40]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[41]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[42]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[43]  Andrey Polyakov,et al.  Implicit Lyapunov-Krasovski Functionals for Stability Analysis and Control Design of Time-Delay Systems , 2015, IEEE Transactions on Automatic Control.

[44]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[45]  Seiichi Nakamori,et al.  Signal estimation with multiple delayed sensors using covariance information , 2010, Digit. Signal Process..

[46]  Zidong Wang,et al.  Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances , 2009 .

[47]  Shankar P. Bhattacharyya,et al.  Robust, fragile, or optimal? , 1997, IEEE Trans. Autom. Control..

[48]  Joaquín Míguez,et al.  A robust scheme for distributed particle filtering in wireless sensors networks , 2017, Signal Process..