On estimation of the parameters in the complex network via the adaptive observer

In this paper, the problem of estimation of the unknown parameters in the complex networks composed of identical nodes being generalized Lorenz chaotic systems will be discussed. The estimation is provided by an adaptive observer. Estimation of the parameters is provided on the complex network with ring topology and bidirectional coupling between nodes. The extra node being an adaptive observer is connected with the permanent node of the analyzed complex network. During the relatively short period, this additional node will be identically synchronized with the analyzed complex network without precise knowledge of the unknown parameters in the permanent nodes. The results are illustrated by the numerical simulation as well.

[1]  Guanrong Chen,et al.  ROBUST STRUCTURAL SYNCHRONIZATION IN DYNAMICAL COMPLEX NETWORKS , 2007 .

[2]  Volodymyr Lynnyk,et al.  Network-based control of nonlinear large-scale systems composed of identical subsystems , 2019, J. Frankl. Inst..

[3]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[4]  Xiaohua Xia,et al.  Adaptive Synchronization for Generalized Lorenz Systems , 2008, IEEE Transactions on Automatic Control.

[5]  Xiang Li,et al.  Fundamentals of Complex Networks: Models, Structures and Dynamics , 2015 .

[6]  Tiedong Ma,et al.  Parameter estimation and topology identification of uncertain general fractional-order complex dynamical networks with time delay , 2016, IEEE/CAA Journal of Automatica Sinica.

[7]  Ling Lü,et al.  Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network , 2011 .

[8]  R. Massey.  From chaos to order? , 1986, Connecticut medicine.

[9]  L. Shilnikov,et al.  NORMAL FORMS AND LORENZ ATTRACTORS , 1993 .

[10]  Takayuki Ishizaki,et al.  Hierarchical decentralized observer design for linearly coupled network systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  Volodymyr Lynnyk,et al.  Synchronization of symmetric complex networks with heterogeneous time delays , 2019, 2019 22nd International Conference on Process Control (PC19).

[12]  Branislav Rehák,et al.  Sum-of-squares based observer design for polynomial systems with a known fixed time delay , 2015, Kybernetika.

[13]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[14]  Guanrong Chen,et al.  Secure synchronization of a class of chaotic systems from a nonlinear observer approach , 2005, IEEE Transactions on Automatic Control.

[15]  Alexander L. Fradkov,et al.  On synchronization in heterogeneous FitzHugh–Nagumo networks , 2019, Chaos, Solitons & Fractals.

[16]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[18]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[19]  Volodymyr Lynnyk,et al.  Design of a nonlinear observer using the finite element method with application to a biological system , 2019 .

[20]  Volodymyr Lynnyk,et al.  On applicability of auxiliary system approach in complex network with ring topology , 2019 .

[21]  Volodymyr Lynnyk,et al.  On detection of generalized synchronization in the complex network with ring topology via the duplicated systems approach* , 2019, 2019 8th International Conference on Systems and Control (ICSC).

[22]  Junqi Yang,et al.  Observer-based state estimation and unknown input reconstruction for nonlinear complex dynamical systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[23]  B. Bollobás.  The evolution of random graphs , 1984 .

[24]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[25]  Yubo Zhang,et al.  Identification of efficient observers for locating spreading source in complex networks , 2016 .

[26]  Daniel Liberzon,et al.  Robust observers and Pecora-Carroll synchronization with limited information , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[27]  Sergej Celikovský,et al.  Adaptive high gain observer extension and its application to bioprocess monitoring , 2018, Kybernetika.

[28]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[29]  Volodymyr Lynnyk,et al.  Decentralized networked stabilization of a nonlinear large system under quantization , 2019, IFAC-PapersOnLine.

[30]  Henk Nijmeijer,et al.  Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters , 2009, Autom..

[31]  Alexander N. Pisarchik,et al.  Synchronization: From Coupled Systems to Complex Networks , 2018 .

[32]  Qinghua Zhang,et al.  Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems , 2002, IEEE Trans. Autom. Control..

[33]  Denis V. Efimov,et al.  Interval state observer for nonlinear time varying systems , 2013, Autom..

[34]  A. Koronovskii,et al.  RESIDENCE TIME DISTRIBUTIONS FOR COEXISTING REGIMES OF BISTABLE DYNAMICAL SYSTEMS SUBJECTED TO NOISE INFLUENCE , 2017 .

[35]  Sergej Celikovský,et al.  Message Embedded Chaotic Masking Synchronization Scheme Based on the Generalized Lorenz System and Its Security Analysis , 2016, Int. J. Bifurc. Chaos.

[36]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[37]  Guanrong Chen,et al.  Robust synchronization of a class of chaotic networks , 2013, J. Frankl. Inst..

[38]  Vladimir Klinshov,et al.  Event-based simulation of networks with pulse delayed coupling. , 2017, Chaos.

[39]  B. Rehák.  Observer Design for a Time Delay System via the Razumikhin Approach , 2017 .

[40]  Henk Nijmeijer,et al.  c ○ World Scientific Publishing Company ADAPTIVE OBSERVER-BASED SYNCHRONIZATION FOR COMMUNICATION , 1999 .

[41]  Faizan Ur Rehman,et al.  Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach , 2018 .

[42]  Christopher Edwards,et al.  Enhancement of adaptive observer robustness applying sliding mode techniques , 2016, Autom..

[43]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .