Analysis and stability of consensus in networked control systems

• Published in: Applied mathematics and computation Vol. 217; no. 3; pp. 988 - 1000
• Main Authors: DeLellis, Pietro, diBernardo, Mario, Garofalo, Franco, Liuzza, Davide
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.10.2010; Elsevier
• Subjects: Acceleration of convergence; Activation; Complex networks; Consensus; Convergence; Dynamics; Exact sciences and technology; Mathematical analysis; Mathematical models; Mathematics; Networks; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Stability; Switching; Switching protocols; Switching theory; Consensus; Complex networks; Switching protocols; Numerical analysis; Convergence acceleration; Applied mathematics; Control system; Convergence rate; Numerical simulation; Numerical stability; Convergence speed
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.01.126

In this paper, the consensus problem in networks of integrators is investigated. After recalling the classical diffusive protocol, we present in a unified framework some results on the rate of convergence previously presented in the literature. Then, we introduce two switching communication protocols, one based on a switching coupling law between neighboring nodes, the other on the conditional activation of links in the network. We show that the former protocol induces the monotonicity of each system in the network, enhancing the speed of convergence to consensus. Moreover, adopting this novel protocol, we are able to control the network, steering the nodes’ dynamics to a desired consensus value. The aim of the latter protocol is instead to select adaptively the activation of the edges of the network, in accordance with the dynamics of the network. After showing the effectiveness of both approaches through numerical simulations, the stability properties of these protocols are discussed.