Consensus under switching spanning-tree topologies and persistently exciting interconnections

Abstract

Abstract-We study the consensus problem for networks with changing communication topology and with time-dependent communication links. That is, the network changes in two dimensions: "geographical" and "temporal". We establish that consensus is reached provided that there always exists a spanning tree for a minimal dwell-time and the interconnection gains are persistently exciting. Our main result covers the particular case, studied in the literature, of one fixed-topology with time-varying interconnections but also that of changing topologies with reliable interconnections during a dwell-time. Another originality of our work lies in the method of proof, based on stability theory of time-varying and switched systems. Simulations on an academic example are provided to illustrate our theoretical results.

Decentralized synchronization of time-varying oscillators under time-varying bidirectional graphs

“…Roughly speaking, the condition (10) states that there must be a minimal dwell-time interval, starting at any time, during which the interconnections are active; for instance, the interconnections cannot vanish for increasing amounts of time. Furthermore, the condition imposed by (11) is the one relating the persistency of excitation of the interconnections to the frequency of oscillation.…”

“…Furthermore, the condition (10) with Ω i = a n (t) holds for any fixed n, but it fails as n increases since the lengths of the intervals over which a(t) = 1 diminish arithmetically. In other words, a(t) is a train of square pulses of 50% duty cycle but of linearly increasing frequency.…”

“…In this context, an interesting challenge arises when the communication is constrained. For instance, when the communication is intermitent or when the graph topology is time-varying, or even when both happen simultaneously [10]. Such a problems have received a considerable attention in the literature starting with [6], [11], where a network of single-integrator systems is considered and the interconnection graph is assumed to be piece-wise constant and to switch between a finite number of undirected and directed graphs, respectively.…”

Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics

“…Considering time-varying graphs captures different scenarios in which the transfer of information among the nodes is unreliable, the information flow through a restricted amount of channels, or, when the nodes have a limited sensing range. Consensus problem under time-varying and switching graphs has been widely studied in the literature, see e.g., [3,[59][60][61][62][63][64][65], mostly for nodes with single or double integrator dynamics, under different graph-connectivity conditions. The approach in the aforementioned references uses non-systematic trajectory-based approaches via non-smooth Lyapunov functions, which makes the analysis of robustness challenging.…”

Modeling and Analysis of Matthew Effect Under Switching Social Networks via Distributed Competition

“…The change of the Laplacian matrix before and after topology switching will cause system fluctuations. Therefore, the product of the state at the switching time and the difference between the Laplacian matrix before and after the switching time is considered to compensate for the impact caused by the switching of the communication network, which is specifically expressed as in [17]. Thus, according to (1), the consensus filter can be reformulated as…”