Control Design For A Class Of Non-homogeneous High Order Uncertain Non-linear Systems

This dissertation investigates the problems of the control design for a class of nonhomogeneous high order uncertain nonlinear systems.From the point of view of theory,nonhomogeneous high order uncertain nonlinear systems have a more general form than strict feedback nonlinear systems that have been extensively researched;From the point of view of practice,nonhomogeneous high order uncertain nonlinear systems include a class of under-actuated,weakly coupled,unstable mechanical systems that are exceptionally difficult to control.Therefore,the investigations of control design for nonhomogeneous high order uncertain nonlinear systems are important.The main contents of this dissertation are composed of the following parts:1.Improve the traditional adding a power integrator method.By constructing a series of auxiliary functions,a new method of adding a integral of the auxiliary function is presented.This method can be used to deal with the nonhomogeneous high order uncertain nonlinear systems,and the traditional adding a power integrator method can be regarded as a special case of the new method.2.This part studies the problem of global stabilization by state feedback for a class of nonhomogeneous high order uncertain nonlinear systems.Under an assumption that the lower bounds of the control coefficients are exactly known,a series of auxiliary functions which contains the nonhomogeneous characteristics of systems are constructed,by using the method of adding a integral of the auxiliary function,the sufficient condition for the existence and recursive design procedure of continuous controller which guarantees the systems global strongly stable is given.3.This part studies the problem of global stabilization by state feedback for a class of singular nonhomogeneous high order uncertain nonlinear systems.Firstly,the coefficient of nonlinear term is decomposed into two parts: a bounded but not differentiable function and a differentiable but maybe unbounded function.Then,by using the method of adding a integral of the auxiliary function,we generalize the restriction on the nonlinear term from the coefficient is zero and the growth rate is limited at the origin to the case of arbitrary nonzero continuous functions4.This part studies the problem of global adaptive stabilization by state feedback for a class of nonhomogeneous high order uncertain nonlinear systems which contains unknown parameter and the lower bounds of the unknown control coefficients.By defining a new unknown parameter,the method of adding a integral of the auxiliary function and adaptive techniques based on tuning function,the recursive design procedure of adaptive controller based on only one parameter which guarantees the systems global strongly stable is given.5.This part studies the problem of global stabilization by state feedback for a class of singular high order uncertain nonlinear systems.By using the method of adding a power integrator and other tools such as Young's inequality,the assumption that the coefficients of nonlinear term growth rate should be limited is removed and the existing results are generalized.