Adaptive Synchronization of Nonlinearly Parameterized Complex Dynamical Networks with Unknown Time-Varying Parameters

A new adaptive learning control approach is proposed for a class of nonlinearly parameterized complex dynamical networks with unknown time-varying parameters. By using the parameter separation and reparameterization technique, the adaptive learning laws of periodically time-varying and constant parameters and an adaptive control strategy are designed to ensure the asymptotic convergence of the synchronization error in the sense of square error norm. Then, a sufficient condition of the synchronization is given by constructing a composite energy function. Finally, an example of the complex network is used to verify the effectiveness of proposed approach

Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays

This paper is aimed at application of the passification based adaptive control to decentralized synchronization of dynamical networks. We consider Lurie type systems with hyper-minimum-phase linear parts and two types of nonlinearities: Lipschitz and matched. The network is assumed to have both instant and delayed time-varying interconnections. Agent model may also include delays. Based on the speed-gradient method decentralized adaptive controllers are derived, i.e. each controller measures only the output of the node it controls. Synchronization conditions for disturbance free networks and ultimate boundedness conditions for networks with disturbances are formulated. The proofs are based on Passification lemma in combination with Lyapunov–Krasovskii functionals technique. Numerical examples for the networks of 4 and 100 interconnected Chua systems are presented to demonstrate the efficiency of the proposed approach

Analysis and Design of Adaptive Synchronization of a Complex Dynamical Network with Time-Delayed Nodes and Coupling Delays

This paper is devoted to the study of synchronization problems in uncertain dynamical networks with time-delayed nodes and coupling delays. First, a complex dynamical network model with time-delayed nodes and coupling delays is given. Second, for a complex dynamical network with known or unknown but bounded nonlinear couplings, an adaptive controller is designed, which can ensure that the state of a dynamical network asymptotically synchronizes at the individual node state locally or globally in an arbitrary specified network. Then, the Lyapunov-Krasovskii stability theory is employed to estimate the network coupling parameters. The main results provide sufficient conditions for synchronization under local or global circumstances, respectively. Finally, two typical examples are given, using the M-G system as the nodes of the ring dynamical network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies, which illustrate the effectiveness of the proposed controller design methods

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology

This paper studies the local and global exponential synchronization of a complex dynamical network with switching topology and time-varying coupling delays. By using stability theory of switched systems and the network topology, the synchronization of such a network under some special switching signals is investigated. Firstly, under the assumption that all subnetworks are self-synchronizing, a delay-dependent sufficient condition is given in terms of linear matrix inequalities, which guarantees the solvability of the local synchronization problem under an average dwell time scheme. Then this result is extended to the situation that not all subnetworks are self-synchronizing. For the latter case, in addition to average dwell time, an extra condition on the ratio of the total activation time of self-synchronizing and nonsynchronizing subnetworks is needed to achieve synchronization of the entire switched network. The global synchronization of a network whose isolate dynamics is of a particular form is also studied. Three different examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results. © 2006 IEEE.published_or_final_versio

Synchronization of Chaotic Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Sampled-Data Control

This paper investigates the synchronization problem for neural networks with leakage delay and both discrete and distributed time-varying delays under sampled-data control. By employing the Lyapunov functional method and using the matrix inequality techniques, a delay-dependent LMIs criterion is given to ensure that the master systems and the slave systems are synchronous. An example with simulations is given to show the effectiveness of the proposed criterion

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin