Abstract
In this work, the second-order Laplacian flow in Euclidean space which is a standard algorithm for consensus of double integrator systems is generalized to the abstract setting of Lie groups. For double integrator systems on a Lie group, by using gradients of Polar Morse functions whose critical points form a discrete subgroup, it is proved that consensus is achieved for almost all initial conditions of the agents whose connectivity is described by a nearest neighbor network. In this general framework, it turns out that the standard Euclidean second-order Laplacian flow and the Kuramoto oscillator are special cases in Euclidean space and the unit circle respectively.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
