Control of a Driftless Bilinear Vector Field on $n$-Sphere
Vijay Muralidharan, Arun D. Mahindrakar, Akshit Saradagi · IEEE Transactions on Automatic Control · 2018
In this paper, we consider a multi-input driftless bilinear system evolving on the n-dimensional sphere Sn. We first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on Sn. For the general framework, we establish the global controllability on Snand propose two linear control laws on Snthat achieve asymptotic stabilization of an equilibrium point with an almost global domain-of-attraction. Further, the asymptotically stable closed-loop system trajectories are shown to be arcs on the geodesics of Snfor a particular choice of the equilibrium point. Next, we propose two linear time-varying control laws to achieve trajectory tracking on Snand show the asymptotic stability of the tracking error. A distributed control is designed for the consensus of multiagent bilinear systems on Snwith an undirected tree as the communication graph. The consensus manifold is shown to have an almost global domain of attraction.