Two decentralized heading consensus algorithms for nonlinear multi‐agent systems

Abstract

Inspired byVicsek's model, in this paper we propose two decentralized heading consensus algorithms for nonlinear multi-agent systems. The first algorithm, called WHCA, can be seen as a weighted Vicsek's model. The second algorithm, named LBHCA, is a leader-follower strategy based on the WHCA. It is proved that, under a well-known connectivity assumption, the algorithm WHCA can ensure almost global consensus of the headings, except for the situation where they are initially balanced. For the LBHCA, the global heading consensus is guaranteed under the same connectivity assumption. Simulation results are provided to justify the proposed algorithms.

Asynchronous Distributed Algorithms for Heading Consensus of Multi‐Agent Systems with Communication Delay

“…In addition, note that for any i ∈ V and k ∈ ℕ. Then, mimicking the proofs of Proposition 1 and Lemma in , we conclude that there exists ν ss ∈ ℝ 2 such that lim k →∞ U ( k ) = 1 N ⊗ ν ss provided that (i.e., ), where 1 N := T ∈ ℝ N ×1 . ▪ Lemma Let cos( β 1 ), cos( β 2 ) ∈ [ a , 1], β 1 , β 2 ∈ ℝ, .…”

“…Combining the two cases, we have, for any k ∈ N, The rest of the proof relies on a reasoning similar to what we used in proving the main result for our previously proposed synchronous heading consensus algorithm WHCA in [32]. Firstly, following exactly what we did to the model (6) in [32], the first system of (16) can be rewritten as:…”

“…The rest of the proof relies on a reasoning similar to what we used in proving the main result for our previously proposed synchronous heading consensus algorithm WHCA in . Firstly, following exactly what we did to the model in , the first system of (16) can be rewritten as: where , with and being the first and second components U i ( k ), Λ( k ) = diag ( D 1 ( k +1 ), D 2 ( k + 1), ··· , D N ( k + 1)), and the ( i , j )‐entry of the N × N matrix A ( k ) has the form…”

Weight balance for directed networks: Conditions and algorithms

“…Among those control strategies, the consensus based control approach is one of the most useful approaches and has been studied extensively in the existing literature [5]- [7], [13], [16], [21]. Roughly speaking, the objective of the consensus problem is to design distributed control laws to drive the agents in a group to agree upon certain quantities of interest [3], [14], [18], [23], and one of the important consensus problems is the so-called average consensus [24], in which the agreement value is the average of the initial values of all the agents. For the widely used linear control strategies, it has been pointed out that the agent group can reach a consensus if and only if the underlying graph has a spanning tree [19], [20], [22].…”

Flocking of multi‐agent dynamical systems with intermittent nonlinear velocity measurements

“…In practice, understanding the mechanisms responsible for the emergence of flocking in animal groups can help develop many artificial autonomous systems such as formation control of unmanned air vehicles, motion planning of mobile robots, and scheduling of automated highway systems . Recently, the problem of flocking control in multi‐agent systems has attracted increasing attention, which can be generally described as how to design distributed feedback algorithms based only on local information to guarantee the whole group to organize into a global flocking behavior .…”