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Criteria for global pinning-controllability of complex networks. (English) Zbl 1153.93329
Summary: We study pinning-controllability of networks of coupled dynamical systems. In particular, we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network. The reference trajectory is generated by an exogenous independent oscillator, and pinned nodes are coupled to it through a linear state feedback. We describe the time evolution of the complex dynamical system in terms of the error dynamics. Thereby, we reformulate the pinning-controllability problem as a global asymptotic stability problem. By using Lyapunov-stability theory and algebraic graph theory, we establish tractable sufficient conditions for global pinning-controllability in terms of the network topology, the oscillator dynamics, and the linear state feedback.
MSC:
93B05Controllability
93D20Asymptotic stability of control systems
93C10Nonlinear control systems
93D05Lyapunov and other classical stabilities of control systems
93B11System structure simplification
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