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Physical Sciences and Mathematics Commons

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Applied Mathematics

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Portland State University

2015

Wave equation

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Full-Text Articles in Physical Sciences and Mathematics

Transients Of Platoons With Asymmetric And Different Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman Sep 2015

Transients Of Platoons With Asymmetric And Different Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, …