Robust Adaptive Control Of Triangle Nonlinear Systems

Since the 1980s, these have been great achievements in the adaptive control of nonlinear systems. Roughly speaking, adaptive control is a control method which can automatically adjust control strategy with the change of parameters and structure of the system. Because nonlinear systems are often complicated systems with unknown parameters and structure, it is difficult to set up their accurate mathematic models. Therefore it is very natural to use the adaptive control for nonlinear systems. The most successful adaptive control theory is the adaptive control theory for the so-called parametric-strict-feedback nonlinear systems (in the thesis, they are named triangular nonlinear systems). Up to the present, the triangular nonlinear systems which have been studied are main those systems with linearly parameterized uncertainties. Only a few papers concern nonlinear systems with nonlinearly parameterized uncertainties. In fact, linear parameterization of uncertainties only is an approximation. If there exist uncertain disturbances, adaptive control needs stronger assumptions. In despite of many important achievements obtained in the adaptive control theory of nonlinear systems, much work has left to be done.In the thesis, the problems of adaptive control of triangular nonlinear systems is considered, which contains triangular nonlinear systems with linearly parameterized uncertainties as well as with nonlinearly parameterized certainties. The main results of the thesis are as follows.1. The robust adaptive tracking of triangular nonlinear systems. We take two classes of disturbance functions for a class of nonlinear systems with nonlinear parameterization and general uncertainties. One has assured upper boundedness, the other hasn't assured upper boundedness. When third-order differential coefficient of uncertain parameter function is boundedness, we bring the adaptive law of uncertain parameter and solve the ε—tracking problem. At the same time, a robust adaptive controller is designed in a backstepping manner for a class of uncertain nonlinear systems with nonlinear parameterization, when the bounded of parameter is unknown.The controller can guarantee global uniform ultimate boundedness. The interrelated results will be shown in detail in the second chapter. Compared to the paper[6], the more abroad uncertain functions are allowed.2 The global adaptive regulation of a class of second-order triangle nonlinear systems. To this day, only a few papers relate to the nonlinear systems with nonlinear parameters. When nonlinear parameterization satisfies certain condition, the problem of the global adaptive regulation is researched, and adaptive laws of uncertain parameters are given. The adaptive laws in the thesis are different to the others. The related results will be shown in detail in the third chapter.3 The nerve network control of a magnetic levitation system. The magnetic levitation systems are important real systems. In the paper[35], the problem of nerve network control is researched without disturbances. In the paper[34], the problem of robust control is researched with disturbances which depend on time. In the thesis, the problem of nerve network control is researched with disturbances which depend on time and state. We approximate an unknown nonlinear parameter by. A PI controller is designed to stabilize the position error of the levitated object .At last, we succeed. The controller can guarantee global uniform ultimate boundedness, good tracking effect and transient performance. The related results will be shown in detail in the fourth chapter.Simulations are given for the control schemes designed in the thesis, and demonstrate the effectiveness and feasibility of all the proposed methods. The proposed methods also solve ε-tracking problem.