In this paper we study th-order 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 th-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.
High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems
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Ren, W., Moore, K. L., and Chen, Y. (December 11, 2006). "High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems." ASME. J. Dyn. Sys., Meas., Control. September 2007; 129(5): 678–688. https://doi.org/10.1115/1.2764508
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