On Global Controllability Of Some Class Of Affine Nonlinear Systems And Its Applications

The controllability of nonlinear systems has been studied extensivelyover the past three decades, and considerable progress has been made ineither analysis or synthesis by introducing some useful methods, includ-ing the well-known differential geometric method. However, most of theexisting results on controllability of nonlinear systems are concerned withlocal controllability.In this report, firstly we will investigate the global controllability of gen-eral planar affine nonlinear systems under locally Lipschitz conditions. Asimple necessary and sufficient condition for global controllability will bepresented. The analysis method is based on some basic facts in planartopology such as the Jordan curve Theorem, and in the geometric theoryof ordinary differential equations including the Poincare-Bendixson Theo-rem. It should be pointed out that this necessary and sufficient condition isessentially one of the main results in author's doctoral thesis, but, here weonly need the weaker locally Lipschitz condition for both system vectorfield and control vector field.Secondly, we will investigate a class of higher dimensional affine non-linear systems with a triangular-like structure and present its necessary andsufficient condition for global controllability. In addition, we also investi-gate the global controllability of some higher dimensional affine nonlinearsystems with multi-controller, and give its necessary and sufficient condi-tion for global controllability.Thirdly, by using above new methods, we will discuss the global asymp-totic controllability (a concept closely related to but somewhat weaker thanthe global stability) of affine nonlinear systems and obtain some similar re-sults.Finally, besides introducing some mathematical examples, we will alsointroduce some practical examples in electrical power system, robot con-trol system and Jet engine system to show the application of our mainresults.