Control Design And Performance Analysis Of High-order Uncertain Nonlinear Systems

The problems of the control design for a class of so-called high-order nonlinear systems have been widely studied by researchers in recent years. From the view point of the system model, high-order nonlinear systems represent a more general form of strict feedback nonlinear systems that have been extensively investigated. On the other hand, high-order nonlinear systems include a class of under-actuated, weakly coupled and unstable mechanical systems which are exceptionally difficult to dominate in practice. Therefore, the investigations of control problems for high-order systems have theoretical and practical meanings. However, the control problems can not be solved by the traditional feedback linearization method or backstepping approach.The dissertation focuses on the investigation of the control design for high-order uncertain nonlinear systems. For several different classes of high-order uncertain nonlinear systems, in virtue of the method of adding a power integrator, flexible adaptive technique and other techniques such as Young's inequality, a smooth state-feedback global adaptive stabilizing controller, a continuous state-feedback global adaptive stabilizing controller, a continuous adaptive practical output tracking controller and a smooth adaptive output feedback stabilizing controller are designed respectively, and detailed design procedures of controllers are provided. In addition, by means of existence and uniqueness theorem for ordinary differential equations, Lyapunov stabilization theorem and Barbalat lemma, the corresponding performance analyses of adaptive controllers designed are given. The main contents of this paper are composed of the following four parts:(â… ) Adaptive state-feedback stabilization for a class of high-order uncertain nonlinear systemsThis part studies the problem of global adaptive stabilization by state-feedback for a class of high-order nonlinear systems with unknown control coefficients. For the control design of this class of systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this part, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing controller for a class of high-order uncertain nonlinear systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback controller, which guarantees that the whole closed-loop system is globally uniformly stable, while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.(â…¡) Adaptive state-feedback stabilization for a large class of high-order uncertain nonlinear systemsThis part investigates the problem of global adaptive stabilization by state-feedback for a class of high-order nonlinear systems with unknown control coefficients and zero dynamics. First, some appropriate unknown parameters are introduced to obtain the updating laws when adapting control design. Then, by the flexible way of combining adding a power integrator with adaptive technique and the idea of changing supply functions, the requirement on the unknown control coefficients is relaxed, and a recursive design procedure is successfully developed to achieve a continuous adaptive stabilizing controller. The controller designed guarantees that all the states of the whole closed-loop system are globally uniformly bounded, while the original system states globally asymptotically converge to zero. Finally, an example is provided to illustrate the correctness of the theoretical results.(â…¢) Adaptive practical output tracking control for a class of high-order uncertain nonlinear systemsThis part studies the problem of adaptive practical output tracking control for a class of high-order uncertain nonlinear systems, which has been investigated under the assumption that the lower bounds of the unknown control coefficients are exactly known. Based on the idea of the new robust adaptive control and the continuous stabilization, this assumption is successfully removed. By means of adding a power integrator, a systematic approach is developed to construct a continuous adaptive practical output tracking controller, which guarantees that all the states of the closed-loop system are globally stable, while the tracking error can be bounded by any given positive number after a finite time. Finally, a simulation example is given to illustrate the correctness of the theoretical results.(â…£) Adaptive output feedback stabilization for a class of second-dimensional high-order uncertain nonlinear systemsThis part investigates the stabilizing problem for a class of uncertain nonlinear systems. First, an appropriate observer is introduced, and then based on adding a power integrator and adaptive technique, a new method is presented to construct a smooth adaptive output feedback controller. The main theoretical results show that the controller designed not only guarantees that all the states of the closed-loop systems are bounded, but also the states of the original system and the observer converge to zero asymptotically.All in all, satisfactory solutions to control problems of high-order uncertain nonlinear systems not only guide the academic research of strict feedback nonlinear control systems, but also will enrich the design methods of traditional controllers.