Rendezvous Control Design for the Generalized Cucker–Smale Model on Riemannian Manifolds

A mean‐field approach for the asymptotic tracking problem of moving continuum target clouds

“…Note that the dynamics of target system (18) is completely decoupled from the tracking particle system (19). Thus, we set 𝑔 = 𝑔(𝑡, 𝑥 * , 𝑣 * ) to be the one-agent distribution function for a large target system (18). Then, by using the standard Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, we have the following linear Vlasov equation for 𝑔:…”

“…These emerging research areas have been popular in diverse science and engineering disciplines. Some explicit examples include a fixed pattern formation with a collision avoidance, 16 stochastic description for a fixed pattern formation, 17 rendezvous design to a fixed common target, 18 interparticle bonding force, 19 vehicle platoons problems, 20,21 and space flight formations. 22 To fix the idea, we begin with a brief description of a multiagent system for target tracking which is a finite mobile point cloud.…”

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

“…For example, the authors studied the rendezvous problem on the sphere in Choi et al 21 Based on the generalized Cuker-Smale model 22 on the Riemannian manifold, some feedback control laws such that rendezvous behavior can be obtained are designed. 23,24 In Li et al, 23 the authors designed rendezvous feedback control laws for double-integrator systems on the unit sphere and hyperboloid such that all particles can converge to a given static target. In case the target is moving, the work of Li et al 24 provided the rendezvous feedback control laws for particles on the compact Riemannian manifolds (e.g., unit sphere and unit circle) and flat Riemannian manifolds (e.g., infinite cylinder and Euclidean space).…”

“…23,24 In Li et al, 23 the authors designed rendezvous feedback control laws for double-integrator systems on the unit sphere and hyperboloid such that all particles can converge to a given static target. In case the target is moving, the work of Li et al 24 provided the rendezvous feedback control laws for particles on the compact Riemannian manifolds (e.g., unit sphere and unit circle) and flat Riemannian manifolds (e.g., infinite cylinder and Euclidean space). For autonomous spacecraft rendezvous and docking, the control on the special Euclidean group SE(3) is investigated.…”