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This book presents two nonlinear control strategies for complex dynamical networks. First, sliding-mode control is used, and then the inverse optimal control approach is employed. For both cases, model-based is considered in Chapter 3 and Chapter 5; then, Chapter 4 and Chapter 6 are based on determining a model for the unknow system using a recurrent neural network, using on-line extended Kalman filtering for learning. The book is organized in four sections. The first one covers mathematical preliminaries, with a brief review for complex networks, and the pinning methodology. Additionally, sliding-mode control and inverse optimal control are introduced. Neural network structures are also discussed along with a description of the high-order ones. The second section presents the analysis and simulation results for sliding-mode control for identical as well as non-identical nodes. The third section describes analysis and simulation results for inverse optimal control considering identical or non-identical nodes. Finally, the last section presents applications of these schemes, using gene regulatory networks and microgrids as examples.

Chaotic dynamics is widely used to design random number generators. This paper aims to study the dynamics of chaotic maps in a digital finite-precision domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are explored in an fixed-point arithmetic domain, using the Logistic map and the Tent map as representative examples, from a new perspective with a corresponding state-mapping network (SMN). In SMN, every possible value is considered as a node and the mapping relationship between any pair of nodes works just like a directed edge. The scale-free properties of SMN are proved. The analytic results can be further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of SMN of a chaotic map in the digital computers can facilitate counteracting the undesirable dynamics degenerations of digital chaotic maps in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

This paper presents a chaos and evolutionary programming (CEP)-based digital redesign scheme. This scheme can determine a practically implementable low-gain digital tracker for global optimization of hybrid uncertain input-delay systems with constraints on states and inputs. The proposed global-optimization searching technique, which was provided in the evolutionary programming together with a chaotic optimization algorithm, is utilized to determine the low-gain digital tracker. This technique takes into consideration the relatively large sampling time and the intersampling behavior for digital control of hybrid input-delay systems with unknown-but-bounded parameter uncertainties. Moreover, the newly developed CEP-based digital redesign scheme provides less conservative results than those obtained by the conventional interval methods. One illustrative example is given to demonstrate the effectiveness of the new scheme compared with the conventional methods.

Journal Article Small-World Topology Can Significantly Improve the Performance of Noisy Consensus in a Complex Network Get access Yuhao Yi, Yuhao Yi 1Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China Search for other works by this author on: Oxford Academic Google Scholar Zhongzhi Zhang, Zhongzhi Zhang * 1Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China *Corresponding author: zhangzz@fudan.edu.cn Search for other works by this author on: Oxford Academic Google Scholar Yuan Lin, Yuan Lin 1Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China Search for other works by this author on: Oxford Academic Google Scholar Guanrong Chen Guanrong Chen 2Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China Search for other works by this author on: Oxford Academic Google Scholar The Computer Journal, Volume 58, Issue 12, December 2015, Pages 3242–3254, https://doi.org/10.1093/comjnl/bxv014 Published: 27 February 2015 Article history Received: 20 February 2014 Revision received: 13 January 2015 Published: 27 February 2015

This paper proposes two spatio-temporal epidemic network models based on popularity and similarity optimization (PSO), called r-SI and r-SIS, respectively, in which new connections take both popularity and similarity into account. In the spatial dimension, the epidemic process is described by the diffusion equation; in the time dimension, the growth of an epidemic is described by the logistic map. Both models are represented by partial differential equations, and can be easily solved. Simulations are performed on both artificial and real networks, demonstrating the effectiveness of the two models.

Despite various measures across different engineering and social systems, network robustness remains crucial for resisting random faults and malicious attacks. In this study, robustness refers to the ability of a network to maintain its functionality after a part of the network has failed. Existing methods assess network robustness using attack simulations, spectral measures, or deep neural networks (DNNs), which return a single metric as a result. Evaluating network robustness is technically challenging, while evaluating a single metric is practically insufficient. This article proposes a multitask analysis system based on the graph isomorphism network (GIN) model, abbreviated as GIN-MAS. First, a destruction-based robustness metric is formulated using the destruction threshold of the examined network. A multitask learning approach is taken to learn the network robustness metrics, including connectivity robustness, controllability robustness, destruction threshold, and the maximum number of connected components. Then, a five-layer GIN is constructed for evaluating the aforementioned four robustness metrics simultaneously. Finally, extensive experimental studies reveal that 1) GIN-MAS outperforms nine other methods, including three state-of-the-art convolutional neural network (CNN)-based robustness evaluators, with lower prediction errors for both known and unknown datasets from various directed and undirected, synthetic, and real-world networks; 2) the multitask learning scheme is not only capable of handling multiple tasks simultaneously but more importantly it enables the parameter and knowledge sharing across tasks, thus preventing overfitting and enhancing the performances; and 3) GIN-MAS performs multitasks significantly faster than other single-task evaluators. The excellent performance of GIN-MAS suggests that more powerful DNNs have great potentials for analyzing more complicated and comprehensive robustness evaluation tasks.