On the Global Controllability for Planar Systems without Explicit Control Curves

The global controllability of planar affine nonlinear systems had already been solved and a necessary and sufficient condition had been obtained. However, there is a formidable shortcoming, i.e., it needs to solve explicitly a nonlinear ordinary differential equations. Generally speaking, this is almost an impossible task. To overcome this shortcoming, this paper presents an easily verified sufficient condition for the global controllability of planar affine nonlinear systems, which does not need to solve explicitly the nonlinear ordinary differential equations. Especially, for polynomial systems, this sufficient condition can be verified by finite algebraic operations of the coefficients of the polynomials. Finally, some examples are given to show the application of the results.