Lars Lidvall: Hybrid Feedback Control on Manifolds

Abstract: In this report we introduce the concept of hybrid feedback control and apply it to smooth manifolds. The problem of obtaining robust global asymptotic stability is desirable for applications, but it is not solvable with standard control techniques for not contractable manifolds. Compact manifolds are not contractable, but the smooth compact connected manifolds SO(2) and SO(3) appear in many autonomous vehicles problems. We will solve the problem of designing a robust global asymptotically stable controller for smooth compact connected manifolds in the framework of hybrid feedback control. This result will be applied to products of SO(2) and SO(3).