Consensus Problem of Second-order Dynamic Agents with Heterogeneous Input and Communication Delays

Abstract

Consensus problem of second-order multi-agent systems with velocity damping term in agent's dynamics is investigated. Based on frequency-domain analysis, decentralized consensus condition, which depends on the input delays, is obtained for the system based on undirected and symmetric graph with heterogeneous input delays. For the system based on directed graph with both heterogeneous input delays and communication delays, decentralized consensus condition, which is dependent on the input delays but independent on the communication delays, is also obtained. Simulations illustrate the correctness of the results.

Formation control with velocity assignment for second-order multi-agent systems with heterogeneous time-delays

“…If the new variablex(t) is appropriately chosen, the formation and velocity errors F e and V e can be represented by the errors x e i and ν e as follows. Lemma 1: Assume that the system ofx(t) defined by (13) achieves consensus with zero velocities, that is…”

“…where U ∈ R n×(n−1) is a matrix such that rank[LU (B − L τ )1 n ] = n. Proof: Letx(t) be the variable defined by (13) with the constant vector x e and value ν e given by (17) Remark 1: Our stance in this paper is to investigate the formation and velocity errors in the original multi-agent system (1) under assumption that the time-delayed system (15) achieves consensus. See other papers for the consensus problems of multi-agent systems with/without time-delays [10], [12], [13].…”

“…See other papers for the consensus problems of multi-agent systems with/without time-delays [10], [12], [13].…”

Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay

“…Further, during the recent years, the stability analysis and control design of time delayed chaotic system has been investigated interestingly. Time delay is very often encountered in different technical systems such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, computer‐based control systems, the wireless and web‐based control systems, communication systems, complex dynamical networks, neural networks, and so on . Some authors proposed theorems on the Lyapunov stability for fractional system without and with delay, in the sense of the Caputo fractional derivative.…”

Second-order consensus in multi-agent systems based on second-order neighbours’ information

“…Hence, more attention has been paid to consensus problems for second-order multi-agent systems (Ren and Atkins 2007;Ren 2008;Yu, Chen, and Cao 2010;Yu, Zheng, Chen, Ren, and Cao 2011;Sun and Guan 2012;Wen, Duan, Yu, and Chen 2012;Xie and Wang 2012;Zhang, Chen, and Yu 2012). Due to the finite speeds of transmission and spreading as well as traffic congestions, second-order consensus with time delays in spreading and communication is also studied extensively (Tian and Liu 2009;Hu and Lin 2010;Liu and Jia 2010;Liu and Liu 2010;Qin, Gao, and Zheng 2011;Yang, Wang, and Zhang 2011;Wu and Fang 2012). So far, there is little work related to improve the convergence rate of second-order multiagent systems.…”