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Register a new userL2 norm performance index of synchronization and optimal control synthesis of complex networks
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Added by
Chao Liu
Publication date
2007
fields
Informatics Engineering
and research's language is
English
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In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means that the network synchronizes faster with lower-overshoot. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an optimal controller is designed, according to the so-called LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network.
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The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can be measured by the range of coupling strength that admits stable synchronization, can be optimized for a given number of nodes and links. Depending on the geometric degeneracy of the Laplacian eigenvectors, optimal networks can be classified into different sensitivity levels, which we define as a networks sensitivity index. We introduce an efficient and explicit way to construct optimal networks of arbitrary size over a wide range of sensitivity and link densities. Using coupled chaotic oscillators, we study synchronization dynamics on optimal networks, showing that cospectral optimal networks can have drastically different speed of synchronization. Such difference in dynamical stability is found to be closely related to the different structural sensitivity of these networks: generally, networks with high sensitivity index are slower to synchronize, and, surprisingly, may not synchronize at all, despite being theoretically stable under linear stability analysis.
In this paper, the problem of pinning control for synchronization of complex dynamical networks is discussed. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that lower cost is achieved by the control scheme of pinning nodes with smaller degrees. Some rigorous mathematical analysis is presented for achieving lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are shown for verification and illustration.
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramotos model in complex networks we determine patterns of meta-stability and calculate the modularity of the partition these patterns provide. The results indicate that the more stable the patterns are, the larger tends to be the modularity of the partition defined by them. This correlation works pretty well in homogeneous networks (all nodes have similar connectivity) but fails when networks contain hubs, mainly because the modularity is never improved where isolated nodes appear, whereas in the synchronization process the characteristic of hubs is to have a large stability when forming its own community.
Network topology plays an important role in governing the collective dynamics. Partial synchronization (PaS) on regular networks with a few non-local links is explored. Different PaS patterns out of the symmetry breaking are observed for different ways of non-local couplings. The criterion for the emergence of PaS is studied. The emergence of PaS is related to the loss of degeneration in Lyapunov exponent spectrum. Theoretical and numerical analysis indicate that non-local coupling may drastically change the dynamical feature of the network, emphasizing the important topological dependence of collective dynamics on complex networks.
The IEEE 802.1 time-sensitive networking (TSN) standards aim at improving the real-time capabilities of standard Ethernet. TSN is widely recognized as the long-term replacement of proprietary technologies for industrial control systems. However, wired connectivity alone is not sufficient to meet the requirements of future industrial systems. The fifth-generation (5G) mobile/cellular technology has been designed with native support for ultra-reliable low-latency communication (uRLLC). 5G is promising to meet the stringent requirements of industrial systems in the wireless domain. Converged operation of 5G and TSN systems is crucial for achieving end-to-end deterministic connectivity in industrial networks. Accurate time synchronization is key to integrated operation of 5G and TSN systems. To this end, this paper evaluates the performance of over-the-air time synchronization mechanism which has been proposed in 3GPP Release 16. We analyze the accuracy of time synchronization through the boundary clock approach in the presence of clock drift and different air-interface timing errors related to reference time indication. We also investigate frequency and scalability aspects of over-the-air time synchronization. Our performance evaluation reveals the conditions under which 1 (mu)s or below requirement for TSN time synchronization can be achieved.
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