Networks Of Dynamical Systems Research Articles

Robust control for a networked direct-drive linear motion control system: Design and experiments

This paper investigates the robust control method for networked dynamic systems and its application for a direct-drive linear motion control system in a network environment. The unavoidable network-induced random delays are modeled as Markov chains. The control object of the linear motion control system in this study is a double-sided linear switched reluctance machine (DLSRM). To tackle the inherent uncertainties in the DLSRM, a robust control strategy is designed by proposing a new Lyapunov function and applying the free-weighting matrix technique. A state feedback robust controller is designed such that the closed-loop direct-drive linear motion control system over a network is stochastically robust stable. The robust controller can be conveniently obtained by solving a set of linear matrix inequalities. The numerical simulation of an angular positioning system is presented to illustrate the effectiveness of the proposed robust control method. Furthermore, the experimental tests on the networked direct-drive linear motion control system verify the practicability of the proposed method.

Optimal singular control for nonlinear semistabilisation

ABSTRACTThe singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton–Jacobi–Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.

Urban landscape units and spatial grid networks of the land, water and mountain system using a multiple factor overlap approach: A lowland case study of Hangzhou City, China

The issue that many Chinese cities follow similar international styles degrades local cultural customs and regional ethnic features, and it is drawing much attention of citizens, governors and designers. Some research has corroborated the effectiveness of correlation and integrity of native urban sceneries, to deal with the above issue. Urban landscape can be regarded as a dynamic network system, comprising some interlinked spots and regions. Based on the current situation and academic proceedings, this research introduced the concept of urban landscape network. By a case study of Hangzhou City construction, this paper conducted a grid analysis of the landscape grid network, and built four sub-networks: natural scenery, historical development, road transportation, and land use. Using variance analysis, correlation analysis, multiple regression analysis, this paper examines the relationship between the four sub-networks, and finally achieved an appropriate regression equation of the landscape network in accordance with the subjective satisfaction evaluation concerning the landscape quality.

Networked Dynamical Systems 2016

Networked Dynamical Systems 2016

Information Transfer and Conformation Change in Network of Coupled Oscillator

Abstract: In this paper, we investigate the problem of conformation change in a network of coupled oscillator system with double well internal potential. Conformation change refers to the phenomena where all the oscillators in the network make a transition from one potential well to another potential well under the influence of external perturbation. We propose a novel approach based on information transfer in network dynamical systems to understand this phenomenon. We consider a heterogeneous network system where the internal dynamics of the oscillators are assumed to be nonidentical and the interconnecting Laplacian can also be asymmetric. The objective is to determine which of the network oscillator is most influential in driving the conformation dynamics. We show that the net information transfer of individual oscillators can be used to determine the most influential oscillator which can drive the entire network from one well to another well of the potential. We use three different network topologies to verify our proposed framework.

Fluctuation-Driven Neural Dynamics Reproduce Drosophila Locomotor Patterns.

The neural mechanisms determining the timing of even simple actions, such as when to walk or rest, are largely mysterious. One intriguing, but untested, hypothesis posits a role for ongoing activity fluctuations in neurons of central action selection circuits that drive animal behavior from moment to moment. To examine how fluctuating activity can contribute to action timing, we paired high-resolution measurements of freely walking Drosophila melanogaster with data-driven neural network modeling and dynamical systems analysis. We generated fluctuation-driven network models whose outputs—locomotor bouts—matched those measured from sensory-deprived Drosophila. From these models, we identified those that could also reproduce a second, unrelated dataset: the complex time-course of odor-evoked walking for genetically diverse Drosophila strains. Dynamical models that best reproduced both Drosophila basal and odor-evoked locomotor patterns exhibited specific characteristics. First, ongoing fluctuations were required. In a stochastic resonance-like manner, these fluctuations allowed neural activity to escape stable equilibria and to exceed a threshold for locomotion. Second, odor-induced shifts of equilibria in these models caused a depression in locomotor frequency following olfactory stimulation. Our models predict that activity fluctuations in action selection circuits cause behavioral output to more closely match sensory drive and may therefore enhance navigation in complex sensory environments. Together these data reveal how simple neural dynamics, when coupled with activity fluctuations, can give rise to complex patterns of animal behavior.

Heterogeneous state estimation in dynamic networked systems

Distributed state estimation refers to a method for computing a local estimate of the global state in each node of a networked systems. Typically, current methods take a homogenous approach, where the same estimator is performed in each node for approximating a centralised estimation result. Yet, many practical examples indicate that the capabilities of a networked systems rise when its nodes do not only have similarities, but, to some extent, differ from each other. Inspired by this idea, this study extends current studies on homogeneous estimation and turns it into a heterogeneous solution for distributed state estimation focusing on three contributions. Firstly, the estimation problem in networked systems is reformulated so that a particular interdependency of the estimation results between any two nodes is pursued rather than aiming for similar estimation results across all nodes. Secondly, a node setup is adopted suiting heterogeneous estimation on system level, yet, still allows for nodes to employ solutions based on existing (homogenous) distributed estimators. Thirdly, the pursued interdependency of local estimation results is proven for the adopted setup, along with practical conditions that will guarantee stable estimation results in each node locally. Extended designs of this heterogeneous estimator are studied for observing the spread of a chemical compound (linear) and for detecting shockwaves on a highway (non-linear).

Gradient systems on coupled cell networks

For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell graph, and we use tools from graph theory to deduce the general form of such functions, relating it to the topological structure of the graph defining the network. The coupling of pairs of dynamical systems cells is represented by edges of the graph, and from spectral graph theory we detect the existence and nature of equilibria of the gradient system from the critical points of the coupling function. In particular, we study fully synchronous and 2-state patterns of equilibria on regular graphs. These are two special types of equilibrium configurations for gradient networks. We also investigate equilibrium configurations of -invariant admissible functions on a ring of cells.

Curate

Curate

Graph-Theoretic Methods for Measurement-Based Input Localization in Large Networked Dynamic Systems

In this paper, we consider the problem of localizing disturbance inputs in first-order linear time-invariant (LTI) consensus networks using measurement-based graph-theoretic methods. We consider every node and edge of the network graph to be characterized with physical weights, and show that the resulting system dynamics can be represented in terms of an asymmetric Laplacian matrix $L_{m}$ . Assuming the network graph to be divided into $p$ coherent clusters, we next propose an input localization algorithm based on the properties of the weak nodal domains corresponding to the first $p-1$ slow eigenvalues of $L_{m}$ . The algorithm takes in sensor measurements of the states from selected nodes, runs a system identification routine to construct the input-output transfer matrix, and compares the signs of the residues of the component transfer functions to a nominal localization key to determine in which cluster(s)the disturbance input may have entered. We prove that for systems defined over a specific class of graphs, referred to as $p$ -area complete graphs, the localization is unique. We also state the extension of this result for second-order synchronization networks. We illustrate the algorithms by applying them to large-scale power system networks.

Collective relaxation dynamics of small-world networks.

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks with regular, small-world, and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N, average degree k, and topological randomness q. We present simplified analytic predictions for the second-largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small, and moderate topological randomness q, including the entire small-world regime. For large q of the order of one, we apply standard random matrix theory, thereby overarching the full range from regular to randomized network topologies. These results may contribute to our analytic and mechanistic understanding of collective relaxation phenomena of network dynamical systems.

Synchronization of chaotic systems.

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.

New results on synchronization control of delayed memristive neural networks

This paper is focused on the exponential synchronization for a class of delayed memristive neural networks. Basing on nonsmooth analysis and control theory, several new sufficient conditions concerning global exponential synchronization are obtained for the proposed system. In addition, the obtained results complement and extend earlier publications on memristive or conventional neural network dynamical systems with continuous or discontinuous right-hand side. Finally, numerical simulations illustrate the effectiveness of our results.

Computation and dissipative dynamical systems in neural networks for classification

Foundational issues related to learning, processing and representation underlying pattern recognition have been discussed in history and in recent times. The scientific approach to pattern recognition could provide new tools to investigate these foundational issues, which in turn could inform the scientific approach to pattern recognition as well. One such tool could be the analysis of learning, processing and representation in connectionist (or neural) networks, which have been extensively used for pattern recognition. Based on a mathematical analysis of the classification behavior of feedforward networks an analysis is given of the empiricist vs. rationalist debate on the possibility or impossibility of induction. The analysis aims to show that forms of induction are possible but not without certain given forms of structure and representation. The analysis is then extended to cover the role of representation in pattern recognition, and the nature of the underlying forms of processing, aiming to show that models of cognition derive from a specific relation between dynamics and computation. These examples illustrate that an interaction between modeling and the discussion on foundational issues could be beneficial for both and could open new avenues in the philosophical and foundational debate not available in previous times.

A Graph-Theoretic Condition for Global Identifiability of Weighted Consensus Networks

In this technical note, we present a sufficient condition that guarantees identifiability for a class of linear network dynamic systems exhibiting continuous-time weighted consensus protocols. Each edge of the underlying network graph ${\cal G}$ of the system is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definition of output distinguishability, we first derive a condition that ensures the identifiability of the edge-weights of ${\cal G}$ in terms of the associate transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge-weights. We describe our results using illustrative examples.

Exponential lag synchronization for delayed memristive recurrent neural networks

In this paper, by using the parallel-memristors connection corresponding to the capacitors and memristors synaptic connection in usual recurrent neural networks, general delayed memristive recurrent neural networks are proposed. Basing on nonsmooth analysis and control theory, several sufficient conditions concerning global exponential lag synchronization are obtained for the proposed system. In addition, the obtained results complement and extend earlier publications on memristive or conventional neural network dynamical systems with continuous or discontinuous right-hand side. Finally, numerical simulations illustrate the effectiveness of our results.

Optimal control for linear and nonlinear semistabilization

The state feedback linear-quadratic optimal control problem for asymptotic stabilization has been extensively studied in the literature. In this paper, the optimal linear and nonlinear control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which involves convergent trajectories and Lyapunov stable equilibria and which is of paramount importance for consensus control of network dynamical systems. Specifically, we show that the optimal semistable state-feedback controller can be solved using a form of the Hamilton–Jacobi–Bellman conditions that does not require the cost-to-go function to be sign definite. This result is then used to solve the optimal linear-quadratic regulator problem using a Riccati equation approach. Finally, two numerical examples are presented to demonstrate the efficacy of the proposed linear and nonlinear semistabilization framework.

Editorial Comment on the Special Issue of “Information in Dynamical Systems and Complex Systems”

This special issue collects contributions from the participants of the “Information in Dynamical Systems and Complex Systems” workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported here in reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

Advances on data, information, and knowledge in the internet of things

The internet of things (IoT) is a dynamic smart networked system with connected sensors, processors, and actuators that are designed to sense and interact with the physical world. Achieving the benefits of IoT requires the fusion and management of large scale heterogeneous data using knowledge-based decision systems and the integration of different technologies. Many challenges exist, including identifying things correctly and safely in IoT, modeling and integrating variety and volumes of data, acquiring knowledge automatically from the big data, and ensuring security and privacy, etc. This theme issue aims to explore these challenges through papers which address: (1) data models and big data and information processing in IoT; (2) how collaboration and interaction in IoT can be facilitated leveraging the best practices developed in social computing, social and community intelligence, and wireless sensor networks; and (3) the security and privacy issues in IoT and mobile computing. This issue is in collaboration with the international workshop on Identification, Information, and Knowledge in the Internet of Things (IIKI2013) held in October 2014, Beijing, China (http://ireg.bnu.edu.cn/IIKI2014/). Following a strict review process, we accept seventeen papers for this theme issue finally. Each of the papers was peer-reviewed by at least two experts in the field. In the following, we provide a brief introduction to each paper. Data dissemination is a challenging issue for mobile social activities in IoT. The paper titled ‘‘strengthen nodal cooperation for data dissemination in mobile social networks’’ by Guoliang Liu et al. proposes an incentive scheme to stimulate the users in a network to be more cooperative for data dissemination by considering selfishness factors of the users. Each node’s ability to fetch messages of a specific kind of interest is evaluated, and every single user can rent other nodes to help with obtaining the interested messages by paying credits. Extensive simulations on real traces are implemented to evaluate the proposed incentive scheme. The paper ‘‘self-Universum support vector machine’’ (SUSVM) by Dalian Liu et al. provides a theoretical explanation for an improved twin support vector machine based on the concept of Universum, which takes the positive class and negative class as Universum separately for the binary classification problem. Furthermore, SUSVM is improved by a special formulate of linear programming, which leads to the better generalization performance and less computational time. Data management and information organization play key roles in IoT realization. Yunchuan Sun et al. propose an extensible and active semantic information organization model for IoT in the paper titled ‘‘An extensible and active semantic model of information organizing for the Internet of Things.’’ The proposed model is well defined and involves two layers: the object layer and the event layer, which are both discussed in detail including the Y. Sun (&) R. Bie Beijing Normal University, Beijing, China e-mail: yunch@bnu.edu.cn

Integrated fault‐tolerant control methodology for non‐linear dynamical networked control systems subject to time‐varying delay

This study deals with the problem of designing an integrated fault-tolerant control (FTC) methodology for non-linear dynamical networked control systems subject to time-varying delay. For the convenience of residual generation, influence caused by network-induced delay is transformed into time-varying uncertainty, which facilitates further manipulation. A fault diagnosis scheme is utilised for fault detection and isolation. On the basis of the uncertainty and fault information obtained by the fault diagnosis procedure, an FTC component is developed to compensate for the effects of uncertainty and fault. In the absence of fault, a nominal controller is employed to deal with the system uncertainty. After fault detection estimator is activated, the controller is reconfigured to guarantee the boundedness of all the system signals until the fault is isolated. After the fault is isolated, the controller is reconfigured to improve the control performance by using the fault information generated by the isolation module. In addition, the stability of the proposed scheme is rigorously investigated. Finally, a simulation example is utilised to illustrate the performance of the proposed scheme.