System of funnels framework for robust global non-linear control

Abstract

There exist various methods for planning nominal trajectories to guide desired behaviours of non-linear systems, along with constructive methods for computing finite-time invariant sets, termed funnels, about locally-stabilized nominal trajectories. In order to achieve a desired behaviour defined by a set of nominal trajectories and their corresponding funnels, one has to switch from one local control to another at the right instances. This paper presents a general hybrid-control framework which is designed for correct switching between locally stabilizing controllers and can be used in conjunction with various approaches for funnel computation. Our framework prescribes exact connectivity co..