Robust Consensus of Multi-agent Systems with Bounded Disturbances

Abstract

Recent years have witnessed an increasing interest in the coordination of distributed multi-agent systems. In this area, one of the most fundamental problems is the consensus problem, which has broad connections with a wide range of disciplines including statistical decision theory [1, 2], distributed computing [3, 4], biology [5, 6], and cooperation of multi-agent systems[7, 8]. Consensus roughly speaking is characterized as a collection of agents with locally sensed information or limited inter-component communications seeking to reach a common value. A basic consensus protocol in the context of multi-agent systems usually consists of a information exchange network, in which each agent updates its state by forming a convex combination of the states of its neighbors and itself. Some sufficient consensus conditions for the heading angles of a group of agents modeled by Vicsek et al. [5] are presented in [9, 10]. Some less restrictive conditions were obtained in [12, 13], where consensus is ensured if there exists a spanning tree in the union of the information exchange networks. Many other generalizations have been devoted to different types of agent dynamics and different topologies of information exchange networks, such as nonlinear consensus protocol [14], consensus of agents modeled by double integrators [15], consensus algorithm with cohesion, separation and alignment rules [16, 17], consensus over random networks [18, 19], consensus of networked agents with time-delays [20, 21]. Most of the previously mentioned references used noise-free state iteration, that is they assume the information exchange between agents is accurate. This assumption would obviously be inappropriate in real distributed systems, since there are various kinds of noises during the sending, transmission and receiving of information. Consensus of distributed systems with noise disturbance is an important challenge, and now there are only a few results. The average-consensus control with fixed topology and additive input noises is investigated in [22], where the long term consensus error is minimized by a least mean square optimization method. [23] considered the consensus protocol with fixed topology and independent identically distributed noises, and used stochastic Lyapunov functions to establish mean square consensus. The extension to the case of time-varying topologies is carried in [24], where some sufficient conditions are given for mean square average-consensus and almost sure consensus. [11] further investigated decentralized adaptive synchronization for a stochastic model with uncertainties. Roughly speaking, the consensus algorithms Robust Consensus of Multi-agent Systems with Bounded Disturbances 15