TRANSITIONS BETWEEN LIMIT CYCLES FOR AN UNDERACTUATED SYSTEM: VIRTUAL CONSTRAINTS APPROACH1

An underactuated mechanical system can be orbitally stabilized to certain limit cycles by the method of virtual constraints. This method results in a time-periodic controller which makes a chosen limit cycle locally exponentially orbitally stable. In this paper, we improve the technique in two ways. Firstly, the time dependence of the controller is removed, and an equivalent purely state-feedback controller is given. Secondly, the restriction of local stability is relaxed by providing a method to transition between different limit cycles of the same system.