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In this paper we study ℓth-order (ℓ⩾3) consensus algorithms, which generalize the existing first-order and second-order consensus algorithms in the literature. We show necessary and sufficient conditions under which each information variable and its higher-order derivatives converge to common values. We also present the idea of higher-order consensus with a leader and introduce the concept of an ℓth-order model-reference consensus problem, where each information variable and its high-order derivatives not only reach consensus, but also converge to the solution of a prescribed dynamic model. The effectiveness of these algorithms is demonstrated through simulations and a multivehicle cooperative control application, which mimics a flocking behavior in birds.
Ren et al. (Mon,) studied this question.