863 research outputs found

    Control of coupled oscillator networks with application to microgrid technologies

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    The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies we study here control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions--a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. Interestingly, the amount of control, i.e., number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself

    Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

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    In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

    Effects of the network structural properties on its controllability

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    In a recent paper, it has been suggested that the controllability of a diffusively coupled complex network, subject to localized feedback loops at some of its vertices, can be assessed by means of a Master Stability Function approach, where the network controllability is defined in terms of the spectral properties of an appropriate Laplacian matrix. Following that approach, a comparison study is reported here among different network topologies in terms of their controllability. The effects of heterogeneity in the degree distribution, as well as of degree correlation and community structure, are discussed.Comment: Also available online at: http://link.aip.org/link/?CHA/17/03310

    Consensus analysis of multiagent networks via aggregated and pinning approaches

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    This is the post-print version of of the Article - Copyright @ 2011 IEEEIn this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.This work was jointly supported by CityU under a research grant (7002355) and GRF funding (CityU 101109)
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