Abstract

In the analysis and design of a multi-agent system (MAS), studying the graph representing the system is essential. In particular, when the communication links in a MAS are subject to uncertainty, a random graph is used to model the system. This type of graph is represented by a probability matrix, whose elements reflect the probability of the existence of the corresponding edges in the graph. This probability matrix needs to be adequately estimated. In this thesis, two approaches are proposed to estimate the probability matrix in a random graph. This matrix is time-varying and is used to determine the network configuration at different points in time. For evaluating the probability matrix, the connectivity of the network needs to be assessed first. It is to be noted that connectivity is a requirement for the convergence of any consensus algorithm in a network. The probability matrix is used in this work to study the consensus problem in a leader-follower asymmetric MAS with uncertain communication links. We propose a novel robust control approach to obtain an approximate agreement among agents under some realistic assumptions. The uncertainty is formulated as disturbance, and a controller is developed to debilitate it. Under the proposed controller, it is guaranteed that the consensus error satisfies the global L2-gain performance in the presence of uncertainty. The designed controller consists of two parts: one for time-varying links and one for time-invariant links. Simulations demonstrate the effectiveness of the proposed methods.