We prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point. Our result shows that many known sufficient conditions can be derived in a unified way from a single general principle, namely, the combination of a nilpotent approximation with the use of input symmetries. A number of new sufficient conditions are obtained. All these results follow from one simple general principle, namely, that local controllability follows whenever brackets with certain symmetries can be 'neutralized,' in a suitable way, by writing them as linear combinations of brackets of a lower degree. Both the class of symmetries and the definition of 'degree' can be chosen to suit the problem.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics