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Event-Triggered Multi-equilibrium Control of Dynamical Networks

Many real networks are made up of few clusters and different clusters often complete different functions. In this paper, the function of each cluster is seemed as an equilibrium point of the isolated dynamics of each node. When the nodes in different clusters achieve different equilibrium points, the network achieves a multi-equilibrium point, i.e. the network is becoming multi-stable. We study here how to control such a network by using event-triggering functions. By adopting a distributed event-triggered control approach, in which piecewise continuous control laws and event-triggering functions are proposed and combined. More precisely, the suggested piecewise continuous control laws only involve local measurements updating at infrequent and inequitably event-triggered instants that are individually determined, and contain partial control actions that are kept constant during updating intervals until the next updating instant. These event-triggered updating instants are determined individually according to given event-triggered functions about the state differences in between the nodes and their corresponding desired equilibrium points. Exponential stability in the closed-loop networks configured via the proposed control strategies is examined by employing the Lyapunov method. Numerical simulations are performed to illustrate the main results.