High-Order Consensus Algorithms in Cooperative Vehicle Systems

In this paper we study l
^th
order (l >= 3) consensus algorithms, which generalize the existing first-order and second-order consensus algorithms in the literature. We will show sufficient conditions under which each information variable and their higher-order derivatives converge to common values. We will present the idea of higher-order consensus with a leader and introduce the concept of an l
^th
order model-reference consensus problem, where each information variable and their high-order derivatives not only reach consensus but also converge to the solution of a prescribed dynamic model. The effectiveness of these algorithms are demonstrated through simulations and a multi-vehicle cooperative control application which mimics flocking behavior in birds.