Mathematical problems for complex networks

Copyright @ 2012 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. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the H∞ fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses. A modified Takagi-Sugeno (T-S) fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. The measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses. Attention is focused on the analysis and design of H∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closed-loop T-S fuzzy control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities, which can be readily solved by using standard numerical software. Two examples are given to illustrate the effectiveness of the proposed design method

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou 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.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.<br /