一类非完整约束系统的镇定与能控性(英文)

Stabilization and Controllability of a Class of Nonholonomic Systems

考虑非完整约束系统的镇定与能控性问题 .文中首先证明了虽然一般地说这类系统不能由光滑反馈镇定 ,但它的存在性依赖于初值 .当初值在一个零测集外时 ,这种反馈镇定确实存在 .然后我们证明了这类系统在分段光滑控制下全局可控 .由于证明是构造性的 ,它给出了相应的控制 .

In this note, the stabilization and controllability of a class of nonholonomic control systems are considered. First of all, it is shown that even though in general a smooth state feedback control, which stabilizes the system, does exist , the existence depends on the initial position of the system. It does exist except a very limited measure_zero set. Then we show that the systems are globally controllable by piecewise smooth controls. As a corollary, the systems are finite time stabilizable by piecewise smooth control. The proofs are constructive so the controls are provided precisely.