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SUMMARYThe problem of second-order consensus is investigated in this paper for a class of multi-agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second-order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second-order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis.

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We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.

This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, a distributed continuous static consensus protocol based on the relative state information is first designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable residual set. A fully distributed adaptive consensus protocol is then designed, which, contrary to the static protocol, relies on neither the eigenvalues of the Laplacian matrix nor the upper bounds of the uncertainties. For the case where there exists a leader whose control input is unknown and bounded, distributed static and adaptive consensus protocols are proposed to ensure the boundedness of the consensus error. It is also shown that the proposed protocols can be redesigned so as to ensure the boundedness of the consensus error in the presence of bounded external disturbances which do not satisfy the matching condition. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.