On bipartite consensus of linear MASs with input saturation over directed signed graphs: Fully distributed adaptive approach

Abstract

This paper studies the bipartite consensus problem with input saturation for general linear represents multi‐agent systems (MASs) with signed digraphs. Based on relative state information among neighbour agents, distributed adaptive protocols and a compensation observer are proposed, wherein both leaderless bipartite consensus and tracking bipartite consensus problems are addressed. For the case only relative output information is available, observer‐based distributed adaptive protocols are also designed, where for each agent, a local observer is given to estimate signed consensus error and a distributed observer is presented to achieve bipartite consensus and generate control input and a compensation observer is designed to handle input saturation. Simulation illustrations are given to explain the feasibility. The control protocols presented in this article depend on only local relative state or output information, without any eigenvalue information of Laplacian matrices associated with signed digraphs, which can be practically used for each agent in a fully distributed way.

Fully distributed observer‐based protocols for bipartite consensus of directed nonlinear multi‐agent systems: A proportional‐integral‐gain perspective

“…Lemma 3 (Nan et al 31,32 ). For a strongly connected antagonistic graph  1 with L s1 ∈ R l×l as the associated signed Laplacian matrix, there exists a positive diagonal matrix R ≜ diag(r 1 , … , r l ) such that min…”

“…where Ls1 = RL s1 + L T s1 R with r = [r 1 , r 2 , … , r l ] T being the left zero feature vector of D 1 L s1 D 1 , 𝜆 1 means the smallest nonzero eigenvalue of Ls1 and D 1 𝜉 denotes any vector with positive entries. Lemma 4 (Nan et al 31,32 ). There exists a diagonal positive matrix G ≜ diag(g 1 , … , g N−l ) such that GL s2 + L T s2 G > 0.…”

Fully distributed bipartite output formation tracking for heterogeneous singular multiagent systems on signed digraphs

“…On the other hand, the agents should be subject to certain constraints, among which input saturation constraint attracts numerous attentions 27,28 . At present, some works focus on the bipartite consensus control subject to input saturation 29‐32 . In order to conquer saturation, Qin et al 29 designed a low‐gain consensus protocol for bipartite consensus of homogeneous MASs with input saturation.…”

“…In order to conquer saturation, Qin et al 29 designed a low‐gain consensus protocol for bipartite consensus of homogeneous MASs with input saturation. Then, the low‐gain technique was further considered by Nan et al, a fully distributed low‐gain protocol with adaptive mechanism was developed for saturated MASs 30 . In the work of Zhu et al, 32 the bipartite consensus problem with input saturation was generalized to singular MASs.…”

A Hybrid Predictive Type-3 Fuzzy Control for Time-Delay Multi-Agent Systems

“…In another paper, a distributed adaptive policy was suggested to analyze MASs subject to sensor attacks [4]. Moreover, a distributed consensus of linear MASs with matching uncertainties was analyzed in [5].…”