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

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Quantized H-Infinity control for nonlinear stochastic time-delay systems with missing measurements

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, the quantized H∞ control problem is investigated for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing. A nonlinear stochastic system with state delays is employed to model the networked control systems where the measured output and the input signals are quantized by two logarithmic quantizers, respectively. Moreover, the data missing phenomena are modeled by introducing a diagonal matrix composed of Bernoulli distributed stochastic variables taking values of 1 and 0, which describes that the data from different sensors may be lost with different missing probabilities. Subsequently, a sufficient condition is first derived in virtue of the method of sector-bounded uncertainties, which guarantees that the closed-loop system is stochastically stable and the controlled output satisfies H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Then, the sufficient condition is decoupled into some inequalities for the convenience of practical verification. Based on that, quantized H∞ controllers are designed successfully for some special classes of nonlinear stochastic time-delay systems by using Matlab linear matrix inequality toolbox. Finally, a numerical simulation example is exploited to show the effectiveness and applicability of the results derived.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Leverhulme Trust of the U.K., the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61028008, 61134009, 61104125, 60974030, and 61074016, and the Alexander von Humboldt Foundation of Germany