Abstract
In this work, we study the local dynamics of control-affine systems that are ‘typical’ in that in an open and dense set of the state space the state vector field does not vanish. After establishing that the ‘local accessible sets’ of points in this set cannot contain a neighbourhood of the initial point, we introduce a number of new geometrical concepts useful in the analysis of local dynamics. The key notion is that of control-transverse objects: submanifolds or foliations transverse to the control distribution. These are shown to locally contain both the case of open-loop and closed-loop controls. We use the Conley index to study variations of the invariant dynamics as the control-transverse object moves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
