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Motivation Stabilization of the nonholonomic systems is a research area attracting much attentionrecently and many physical nonhoionomic systems are subject to stochasticdisturbances which are characterized as impossible precise prediction but knownstatistical properties．The characteristic of．the stochastic disturbances makes itreasonable to model the nonholonomic systems with stochastic disturbances or withunknown covariance stochastic disturbances by stochastic differential equations．Theobjective of our work is to analyze the stabilization of the systems above and designthe almost asymptotic stabilizers in probability for the nonholonomic systems．Thediscontinuous feedback control law,switch control law,and backstepping techniqueare employed throughout the procedure of the research to propose the satisfactorycontrollers while the adaptive control law is adopted for the uncertainty of thediscussed systems．
In conclusion，with the control inputs designed in this thesis，the nonhotonomicsystems with stochastic disturbances or with unknown covariance stochasticdisturbances will be almost asymptotically stabilized in probability．
Organization of this thesis
As it shows，the background and the recent researches both about nonholonomicsystems and stochastic systems which are the two bases of our work are reviewed inFor the detailed work，the nonholonomic systems with stochastic disturbances arediscussed in Chapter 3．First，the model of nonholonomic systems with stochasticdisturbances and the almost global asymptotical stability definitions with stochasticnoise are given in Section 3．1．Then．in Section 3．2 x<,0>-subsystem is dealt and thecontrol law“o is designed to almost globally asymptotically stabilize the state x<,0>in probability at both the singular x<,0>(t<,0>)=0 case and the non-singular x<,0>(t<,0>)≠0case，and when x<,0>(t<,0>)≠0 it is discussed in an open and dense set．The so-calledswitching control law is presented in this section too．In Section 3．3，the state scalingtechnique for the discontinuous feedback is presented．The discontinuous feedbackcontrol law u<,1> is designed for the rest(x<,1>，x<,2>，…，x<,n>)-subsystem by usingbackstepping design procedure for both different u<,0> under the singular x<,0>(t<,0>)=0case and the non-singular x<,0>(t<,0>)≠0 case in Section 3．4．The main result：switchingcontrol law is stated and discussed in this part．In section 3．5 the proposed designmethod is applied to physical systems and the simulation results are presentedWhat’s more，the nonholonomic systems with unknown covariance stochasticdisturbances are discussed in Chapter 4．The same as the previous Chapter,in Section4．1，x<,0>-subsystem is dealt and the control law u<,0> is designed to almost globallyasymptotically stabilize the state x<,0> in probability at both the singular x<,0>(t<,0>)=0case and the non-singular x<,0>(t<,0>)≠0 case，and when x<,0>(t<,0>)≠0 it is discussed in anopen and dense set．The so-cal led switching control law is also presented in thissection．The state scal ing technique for the discontinuous feedback is presented inSection 4．2．The discontinuous feedback adaptive control law u<,1> for the rest(x<,1>，x<,2>，…，x<,n>)-subsystem is designed in Section 4.3 by using backstepping designprocedure for both different u<,0> under the singular x<,0>(t<,0>)=0 case and thenon-singular x<,0>(t<,0>)≠0 case．The main result：switching control law is stated anddiscussed in this part．In section 4.4 the proposed adaptive design method is applied tophysical systems and the simulation results are presented．
Chapter 5 summarizes this thesis and discusses the future work which can beresearched based on the results of this thesis．