Weighted average consensus problem in networks of agents with diverse time-delays

Abstract

This paper studies the weighted average consensus problem for networks of agents with xed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some suf cient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.

Scaled consensus for multi-agent systems with communication time delays

“…First, the scale in the scaled consensus can be negative or positive, however, the weight in the weighted consensus must be positive. Second, the weighted consensus is often mentioned as the weighted average consensus (Li and Ding, 2008; Mei, 2015; Wenhui et al, 2014). The weighted average consensus means that lim t → ∞ x i ( t ) = ∑ j = 1 N w j x j ( 0 ) , i = 1,2,…, N , w j > 0, which implies that all states of agents converge to a common value but the common value is related to the initial data of all agents.…”

“…The aim of the consensus is to design a distributed protocol via local information from its neighbours, to guarantee that all agents can reach an agreement state. The consensus problem has been widely studied and many types of systems have been considered, for example multi-agent systems with first-order dynamics (Altafini, 2013; Jadbabaie et al, 2003; Lin and Jia, 2011; Meng et al, 2015; Olfati-Saber and Murray, 2004; Ren and Beard, 2005; Wenhui et al, 2014), second-order dynamics (Huang et al, 2016; Tang et al, 2012), high-order dynamics (Qiu et al, 2016), general linear dynamics (Chen and Yang, forthcoming; Davis et al, 2013; Ma and Zhang, 2010; Qin and Yu, 2013; Valcher and Misra, 2014; Wang et al, 2013, 2014), non-linear dynamics (Mei, 2015; Peng et al, 2014, 2013; Zhang and Lewis, 2012) and stochastic dynamics (Cheng et al, 2011; Li and Zhang, 2009; Xing et al, forthcoming). However, in many practical networks, the requirement that all states converge to a common value cannot meet human’s need.…”

Extended Gersgorin Theorem-Based Parameter Feasible Domain to Prevent Harmonic Resonance in Power Grid

“…By estimating the distribution range of eigenvalues using matrix elements, a new way to evaluate PFD may be possible without precise eigenvalue computations. In the research works of control engineering area, eigenvalue estimation is used to derive the sufficient condition of the stability of dynamic system in accordance with Lyapunov stability theory and Gersgorin theorem [10][11][12][13][14][15]. Further, the above thought is applied to study the small-disturbance stability of distribution systems with a high proportion of distributed generations in [16].…”