Scaled-Type Consensus

In this chapter, the practical mean-square scaled-consensus problem of multiagent systems is studied. First, higher-order general linear dynamics is investigated, where all agents are subject to faults or denial-of-service attacks (DoS). The considered network comprises agents taking quantized states under undirected communication channels. Different from the existing works, no strict conditions have been imposed on the eigenvalues of the agents’ state matrix. First, we propose a distributed scaled-consensus protocol that utilizes a probabilistic quantization algorithm. Second, scaled-disagreement analysis is provided via mean-square stability methodology. Sufficient conditions in terms of linear matrix inequalities are presented in order to obtain scaled-consensus gain for both leaderless and leader–follower cases. Next, the scaled group consensus problem is investigated over directed graphs. In terms of an appropriate Lyapunov function, sufficient conditions are derived to guarantee scaled consensus for high-order continuous-time systems for strongly connected networks. For the case where the agents are subject to exogenous inputs, scaled consensus is achieved with a guaranteed H₂ / H_∞ performance. Moreover, the problem of the scaled-consensus problem for multiagents under Denial-of-Service (DoS) attack is investigated. The considered attack model allows the adversaries to compromise agents independently. Decay rates for each attack mode are obtained based on a set of linear matrix inequalities. Sufficient conditions in terms of decay rates are derived to guarantee secure scaled consensus. Simulation examples are also given to demonstrate the effectiveness of the proposed theoretical results.