A system S of vector fields is locally controllable at point p if, for every positive time t, the set of points reachable from p by an S-trajectory in time less than equivalent to t contains p in its interior. Let K be the convex hull of the values X(p) of those X belonging to S for which X(p) does not equal 0. It is well known that S is 1. c. at p if o belongs to interior (K), and that S is not 1. c. at p if 0 does not belong to K. It is proved that these are the only cases in which it is possible to determine if S is 1. c. at p by just looking at the values at p of the elements of S. A sufficient condition is proved for local controllability which gives new information for the case when 0 belongs to K but 0 does not belong to interior (K).
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics