15.1.3 Controllability

Now suppose that a system $ {\dot x}=
f(x,u)$ is given on a smooth manifold $ X$ as defined throughout Chapter 13 and used extensively in Chapter 14. The system can be considered as a parameterized family of vector fields in which $ u$ is the parameter. For stability, it was assumed that this parameter was fixed by a feedback plan to obtain some $ {\dot x}= f(x)$. This section addresses controllability, which indicates whether one state is reachable from another via the existence of an action trajectory $ {\tilde{u}}$. It may be helpful to review the reachable set definitions from Section 14.2.1.


Steven M LaValle 2012-04-20