The rendezvous dynamics under linear quadratic optimal control

This paper investigates the dynamics of networks of systems achieving rendezvous under linear quadratic optimal control. While the dynamics of rendezvous were studied extensively for the symmetric case, where all systems have exactly the same dynamics (such as simple integrators), this paper investigates the rendezvous dynamics for the general case when the dynamics of the systems may be different. We show that the rendezvous is stable and that the post-rendezvous dynamics of the network of systems is entirely defined by the common eigenvalues with common eigenvectors output image. The approach is also extended to the case of constraints on systems states, inputs, and outputs.