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

The consensus of non-linear agents under switching topology using dynamic inversion in the presence of communication noise and delay

In this study, a consensus protocol for non-linear multi-agent systems using the non-linear dynamic inversion (NDI) technique is presented. It is named as distributed NDI or DNDI. The agents are considered to be working in a randomly changing environment which is realistic. The randomness in the operating environment is introduced by random switching communication topology, delays, and noise. The consensus protocol is obtained as a closed-form expression, which is a critical requirement for real-time implementation. Also, various cases regarding the communication issues have been considered to study the performance of the DNDI controller. The simulation results are found to be satisfactory

Synchronous MDADT-Based Fuzzy Adaptive Tracking Control for Switched Multiagent Systems via Modified Self-Triggered Mechanism

In this paper, a self-triggered fuzzy adaptive switched control strategy is proposed to address the synchronous tracking issue in switched stochastic multiagent systems (MASs) based on mode-dependent average dwell-time (MDADT) method. Firstly, a synchronous slow switching mechanism is considered in switched stochastic MASs and realized through a class of designed switching signals under MDADT property. By utilizing the information of both specific agents under switching dynamics and observers with switching features, the synchronous switching signals are designed, which reduces the design complexity. Then, a switched state observer via a switching-related output mask is proposed. The information of agents and their preserved neighbors is utilized to construct the observer and the observation performance of states is improved. Moreover, a modified self- triggered mechanism is designed to improve control performance via proposing auxiliary function. Finally, by analysing the re- lationship between the synchronous switching problem and the different switching features of the followers, the synchronous slow switching mechanism based on MDADT is obtained. Meanwhile, the designed self-triggered controller can guarantee that all signals of the closed-loop system are ultimately bounded under the switching signals. The effectiveness of the designed control method can be verified by some simulation results

Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback

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