Stabilization of Stochastic Nonholonomic Systems

【摘要】： There are so many researches about nonholonomic systems and stochastic systems, respectively. However, there is no research considering the nonholonomic systems with disturbances as stochastic systems. With respect to the physical systems, it is reasonable to regard the external and unmodelled disturbances as stochastic disturbances. So here, we first model the nonholonomic systems with stochastic disturbances by stochastic differential equations. In this thesis, the stabilization problem of nonholonomic systems with stochastic disturbances or with unknown covariance stochastic disturbances is considered. The objective is to design the almost global asymptotical controllers in probability u 0 and u1 to stabilize the systems modelled by stochastic differential equations. Firstly, the nonholonomic systems with stochastic disturbances are considered. The control input u 0 is designed to almost asymptotically stabilize in probability the x_0 -subsystem both at the singular case x_0 (t_0) = 0 and at the non-singular case x_0 (t_0)≠0 by using switch control law. Then, the state scaling is introduced for discontinuous feedback control law when dealing with the ( x_1 , x_2 ,…, x_n)-subsystem. According to this, the discontinuous feedback control law, together with the backstepping technique, is adopted to almost asymptotically stabilize in probability the ( x_1 , x_2 ,…, x_n)-subsystem under both different u 0 at two initial states: the singular x_0 (t_0) = 0 case and the non-singular x_0 (t_0)≠0 case. Secondly, the nonholonomic systems with unknown covariance stochastic disturbances are dealt. The design procedure is the same as the above. What’s more is