Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

Abstract

This work explores the edge agreement problem of second-order multi-agent system with dynamic quantization under directed communication. To begin with, by virtue of the directed edge laplacian, we derive a model reduction representation of the closed-loop multi-agent system depended on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent system under directed graph are considered. Motivated by the observation that the static quantizer always lead to the practical stability rather than the asymptotic stability, the dynamic quantized communication strategy referring to the rooming in-rooming out scheme is employed. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent system under dynamic quantized effects with only finite quantization level can be guaranteed.Finally, simulation results are provided to verify the theoretical analysis. under directed communication, rather than undirected topology, is considered.

Distributed Control for Leader-Following Consensus Problem of Second-Order Multi-Agent Systems and Its Application to Motion Synchronization

“…To overcome the shortcomings of two static quantizers, which are static and have large errors under specific conditions, the newly proposed adaptive dynamic quantizer combines the logarithmic quantizer and the uniform quantizer by introducing dynamic gain parameters, and gives the boundary conditions. The error of the newly proposed adaptive dynamic quantizer is less than that of the dynamic uniform quantizer [25] when the input of system is small, and which is equal to that of the dynamic uniform quantizer when the input of system is large. Generally speaking, the quantization error of this quantizer has dynamic quantization interval, limited quantization level and small quantization error compared with the logarithmic quantizer [26], uniform quantizer [27] and dynamic uniform quantizer.…”

“…To describe our control law, denote the adjacency matrix of digraph g by A = a ij ∈ R (N+1)×(N+1) where a ii = 0, a ij = 1 ⇔ (j, i) ∈ , and a ij = 0 ⇔ (j, i) / ∈ for i, j = 0, 1, ..., N. According to the paper [25], we can get the following control law:…”

“…where −Ľ is Hurwitz, the matrix η and θ are calculated by linear matrix inequality θ = −Ľη − ηĽ T , obtain as follows: The error of the novel adaptive dynamic quantizer is less than that of the dynamic uniform quantizer proposed in [25]. To show more clearly, we simplify the leader-following system as follows:…”

“…We get the error comparison between the two dynamic quantizers, as shown in Figure 5. Let e1 = q χ (u) − u, e2 = q µ (u) − u, e1 and e2 are the quantization errors under the action of the new adaptive dynamic quantizer and uniform quantizer [25], respectively. Figure 5 show the comparison between the quantization error of the newly proposed dynamic quantizer and the quantization error of the dynamic uniform quantizer in the system (51).…”

Synchronization of Coupled Harmonic Oscillators Using Quantized Sampled Position Data

“…By using probabilistic versus deterministic quantizers, the quantized consensus problem for multiagent systems is studied in [15]. Moreover, event-triggered consensus [16], averaging consensus [17], consensus tracking [18], metropolis consensus [19], containment control [20], and other consensus problems [21][22][23] affected by data quantization are discussed in recent papers.…”