Global Adaptive Stability Control Design For Several Classes Of Uncertain Nonlinear Systems

The dissertation mainly focuses on the investigation of the global adaptive state feedback stabilization for several types of uncertain nonlinear systems includ-ing high-order uncertain nonlinear systems, high-order uncertain nonholonomic systems and high-order uncertain stochastic nonlinear systems. Moreover, the global state feedback stabilization for the high-order uncertain nonlinear systems with double control input channels and the global output feedback stabilization for high-order uncertain stochastic nonlinear systems are also investigated. For details, the main content of the dissertation consists of the following five parts:(I) Adaptive stabilization for high-order nonlinear systems without overparameterizationThis part is Chapter3of the dissertation, and studies the global adaptive stabilization via state feedback for a class of high-order nonlinear systems with unknown control coefficients. Different from the existing relative results, by skill-fully defining a new unknown design parameter, and applying the properties of the unknown parameter, the method of adding a power integrator and the tuning function based adaptive techniques, a recursive adaptive control design method is successfully presented in which only one-dimension dynamic compensator is required. In terms of the analysis method of Lyapunov stability and Barbalat Lemma, we can prove that under the designed continuous adaptive state feedback controller, the closed-loop system state is bounded and the original system state converges to the origin. Therefore, comparing with the existing results, the pro-posed control design method not only preserves the same control performance, but also obviously reduces the dimension of the required dynamic compensator (from at leat n+1to1).(II) Stabilization for high-order nonlinear systems with double con-trol input channelsThis part is Chapter4of the dissertation, and studies the global state feed-back stabilization for a class of high-order nonlinear systems with double control input channels. Different from the existing results, the scalar control input effects the systems via two scalar differential equations, which makes the structure of sys-tem be somewhat complicated and the stabilization problem can not be directly solved through the existing design methods. By introducing a proper input feed-back transformation, we successfully present a continuous state feedback recursive control design method under some proper restrictions on the system nonlinearities. Moreover, the global asymmetric stability of the closed-loop system is analyzed by using the method of Lyapunov stability and input-to-state stability theories. The results obtained in this part can play a guidance and motivation role to solve the control design problem for the general nonlinear systems with more than one control input channel.(III) Adaptive stabilization for high-order nonholonomic systems with unknown control coefficientsThis part consists of Chapters5and6of the dissertation, and investigates the global adaptive stabilization via state feedback for the high-order nonholo-nomic systems with unknown control coefficients. Chapter5considers the simple case without nonlinear drifts, for which the control design is relatively somewhat simple, but the results gained will paly a guidance role for the case with the un-known nonlinear drifts which is considered in Chapter6. For details, in chapter5, by defining a new unknown design parameter, and introducing an appropriate discontinuous state transformation, a simple switching strategy based adaptive stabilizing control design method is provided. In Chapter6, because of the pres-ence of the nonlinear drifts, we need define two unknown design parameters, and the required switching strategy also becomes more complicated. By flexibly com-bining the method of adding a power integrator and the adaptive techniques, an adaptive recursive control design method is provided in which two-dimension dy-namic compensator is sufficient. Moreover, we also rigorously prove that under the designed continuous controller, the closed-loop system state is globally bounded, and the original system state asymmetrically converges to the origin.(IV) Adaptive state feedback stabilization for high-order stochastic nonlinear systemsThis part is Chapter7of the dissertation, and considers the global adaptive stabilization via state feedback for a class of high-order stochastic systems with unknown control coefficients. For details, in Chapter7, we first discuss the stabil- ity concepts of stochastic nonlinear systems, and generalize the existing stochastic stability concepts to make them be applicable to the general stochastic nonlinear systems with more than one solutions. Correspondingly, the sufficient conditions for the stability concepts are presented to provide the theoretical basis for in-vestigating the stability of the general continuous stochastic nonlinear systems. Second, for the stabilization problem, by defining a new design parameter, intro-ducing a novel control Lyapunov function, and applying the method of adding a power integrator and the tuning function based adaptive design techniques, a con-tinuous adaptive control design method is presented for the system. The designed controller such that the closed-loop system state is bounded almost surely and the original system state converges to the origin almost surely.(â…¤) Output feedback stabilization for high-order stochastic nonlin-ear systemsThis part is Chapter8of the paper, and in terms of the stability concepts and criterion established in Chapter7, considers output feedback stabilization for a class of high-order stochastic systems with unknown control coefficients. By introducing a appropriate state transformation within a static rescaling factor and the unknown control coefficients, and constructing a proper nonlinear observer, a continuous output feedback control design method, which is based on the certainty equivalence principle, is presented for the system. It is worthy pointing out that under the designed output feedback controller, the closed-loop system is globally asymptotically stable in probability.For the theoretical results obtained in the above five parts, the corresponding simulation examples are presented to illustrate the effectiveness and feasibility of the proposed controller design methods.