The Controllability of Bilinear Systems. Part I. Complete Controllability Homogeneous Systems in R2-(0)

摘要

This report may be seen as a part of a continuing effort to address some typical problems of nonlinear control, initially in settings simple enough to permit complete solutions based upon algebraic statements involving system parameters. It is felt that much more effort of this nature will be required before the fruit of theoretical work in nonlinear control theory becomes useful or even accessible for application in practical situations. This report is organized as follows. A preliminary discussion of techniques and terminology is given in section 2. The question of complete controllability is resolved in section 3. In section 4 we consider a variety of related controllability concepts. Future reports will concern the nature of reachable sets when controllability fails, as well as similar results for general bilinear systems on the plane.