$H_{\infty }$ State Estimation for Discrete-Time Delayed Systems of the Neural Network Type With Multiple Missing Measurements

This paper investigates the H state estimation problem for a class of discrete-time nonlinear systems of the neural network type with random time-varying delays and multiple missing measurements. These nonlinear systems include recurrent neural networks, complex network systems, Lur'e systems, and so on which can be described by a unified model consisting of a linear dynamic system and a static nonlinear operator. The missing phenomenon commonly existing in measurements is assumed to occur randomly by introducing mutually individual random variables satisfying certain kind of probability distribution. Throughout this paper, first a Luenberger-like estimator based on the imperfect output data is constructed to obtain the immeasurable system states. Then, by virtue of Lyapunov stability theory and stochastic method, the H∞ performance of the estimation error dynamical system (augmented system) is analyzed. Based on the analysis, the H∞ estimator gains are deduced such that the augmented system is globally mean square stable. In this paper, both the variation range and distribution probability of the time delay are incorporated into the control laws, which allows us to not only have more accurate models of the real physical systems, but also obtain less conservative results. Finally, three illustrative examples are provided to validate the proposed control laws.

[1]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[2]  Hamid Reza Karimi,et al.  $H_{\infty}$ Consensus and Synchronization of Nonlinear Systems Based on A Novel Fuzzy Model , 2013, IEEE Transactions on Cybernetics.

[3]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[4]  Rathinasamy Sakthivel,et al.  Robust state estimation for discrete-time BAM neural networks with time-varying delay , 2014, Neurocomputing.

[5]  Marat Akhmet,et al.  Chaotic period-doubling and OGY control for the forced Duffing equation , 2012 .

[6]  Xibing Kang,et al.  Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays. , 2013, ISA transactions.

[7]  Meikang Qiu,et al.  ${\rm H}_{\infty}$ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  C. Karlgaard,et al.  Robust state estimation using desensitized Divided Difference Filter. , 2013, ISA transactions.

[9]  Hamid Reza Karimi,et al.  Robust H∞ synchronization of a hyper-chaotic system with disturbance input , 2013 .

[10]  Chang-Hua Lien,et al.  Robust H∞ filter design for discrete-time switched systems with interval time-varying delay and linear fractional perturbations: LMI optimization approach , 2013, Appl. Math. Comput..

[11]  Carlos E. de Souza,et al.  Robust Hinfinity filter design for a class of discrete-time parameter varying systems , 2009, Autom..

[12]  Jianwei Zhang,et al.  A Survey on CPG-Inspired Control Models and System Implementation , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Huijun Gao,et al.  State estimation for discrete-time neural networks with time-varying delays , 2008, Neurocomputing.

[14]  Yeong-Jeu Sun,et al.  Robust tracking control of uncertain Duffing–Holmes control systems , 2009 .

[15]  Ming Wang,et al.  Control of Yaw and Pitch Maneuvers of a Multilink Dolphin Robot , 2012, IEEE Transactions on Robotics.

[16]  Yuanqing Xia,et al.  New Results on H∞ Filtering for Fuzzy Time-Delay Systems , 2009, IEEE Trans. Fuzzy Syst..

[17]  Weihua Sheng,et al.  ${\rm H}_{\infty}$ Output Tracking Control of Discrete-Time Nonlinear Systems via Standard Neural Network Models , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Rathinasamy Sakthivel,et al.  Robust h ∞ control for uncertain discrete-time stochastic neural networks with time-varying delays , 2012 .

[19]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[20]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[21]  Choon Ki Ahn,et al.  Takagi-Sugeno fuzzy receding horizon H∞ chaotic synchronization and its application to the Lorenz system , 2013 .

[22]  Asok Ray,et al.  Output Feedback Control Under Randomly Varying Distributed Delays , 1994 .

[23]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[24]  Keum W. Lee,et al.  Robust Control of Chaos in Chua’s Circuit Based on Internal Model Principle , 2007 .

[25]  Haibo Jiang,et al.  Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems , 2011 .

[26]  Meiqin Liu,et al.  H∞ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model. , 2012, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[27]  Jinde Cao,et al.  Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay , 2011, Neural Networks.

[28]  Pagavathigounder Balasubramaniam,et al.  Robust state estimation for discrete-time genetic regulatory network with random delays , 2013, Neurocomputing.

[29]  M. Yahyazadeh,et al.  Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. , 2011, ISA transactions.

[30]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[31]  Ju H. Park,et al.  Synchronization of discrete-time neural networks with time delays subject to missing data , 2013, Neurocomputing.

[32]  Feng Liu,et al.  A new chaotic Hopfield neural network and its synthesis via parameter switchings , 2013, Neurocomputing.

[33]  Hongjie Li,et al.  H∞ cluster synchronization and state estimation for complex dynamical networks with mixed time delays , 2013 .

[34]  Meikang Qiu,et al.  Robust H∞ fusion filtering for discrete-time nonlinear delayed systems with missing measurement , 2010, Proceedings of the 2010 American Control Conference.

[35]  Weihua Sheng,et al.  Exponential H∞ Synchronization and State Estimation for Chaotic Systems Via a Unified Model , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Complex Networks With Uncertain Inner Coupling and Incomplete Measurements , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Zidong Wang,et al.  State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case , 2009, IEEE Transactions on Neural Networks.