Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences

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

From data and structure to models and controllers

Systems and control theory deals with analyzing dynamical systems and shaping their behavior by means of control. Dynamical systems are widespread, and control theory therefore has numerous applications ranging from the control of aircraft and spacecraft to chemical process control. During the last decades, a series of remarkable new control techniques have been developed. The majority of these techniques rely on mathematical models of the to-be-controlled system. However, the growing complexity of modern engineering systems complicates mathematical modeling. In this thesis, we therefore propose new methods to analyze and control dynamical systems without relying on a given system model. Models are thereby replaced by two other ingredients, namely measured data and system structure. In the first part of the thesis, we consider the problem of data-driven control. This problem involves the development of controllers for a dynamical system, purely on the basis of data. We consider both stabilizing controllers, and controllers that minimize a given cost function. Secondly, we focus on networked systems. A networked system is a collection of interconnected dynamical subsystems. For this type of systems, our aim is to reconstruct the interactions between subsystems on the basis of data. Finally, we consider the problem of assessing controllability of a dynamical system using its structure. We provide conditions under which this is possible for a general class of structured systems

Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network

In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the short-term $x(t+6)$. The performance prediction was evaluated and compared with another studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute uncertainties of predictions for noisy Mackey--Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level ($\sigma_{N}$) from 0.01 to 0.1.Comment: 11 pages, 8 figure