Stability And Tracking Control For A Class Of Nonlinear Systems With Unknown Control Directions

In recent several decades, the study of nonlinear systems with unknown directions has always been one of the focuses in control filed, especially after the method of N ussbaum has been found. Consequently, the researchers have paid great attention to this method, and some research achievements have been achieved. However, the control result of the Nussbaum method could be improved. This thesis is devoted to investigated the stability and given tracking accuracy control problems of nonlinear systems with unknown directions. A special method is proposed to study a class of nonlinear systems. De tails is listed as follows.1. Chapter 3 investigated the asymptotic stable problem for a class of nonlinear systems with multiple unknown control directions. A series of virtual controllers have been designed by the backstepping method to obtain an adaptive switching controller. The innovation of this method is to list all possible values of the unknown control directions. The controller contains a switching parameter which will choose the correct control directions when it traverses the given combination sequence. It has been proved that this parameter is bounded and the states of system are globally asymptotic stable.2. Chapter 4 relaxed the conditions of the systems in chapter 3 and discussed the global finite-time stabilization of this systems detailedly. Based on the method of proposed in chapter 3, using a new Lyapunov function, the new logic switching rule and the controller have been constructed. Finally, it is proved that the states of nonlinear systems are bounded and globally finite-time stable.3. In chapter 5, the control strategy proposed in the chapter 3 has been extended to the tracking control problem. This chapter considered a class of high-order nonlinear systems with unknown directions and disturbance. Under some assumptions, using the backstepping method and Lyapunov function, the logic switching rule and the adaptive switching controller would be designed. It has been proved that this controller guarantees all the system signals are bounded and the tracking error converges to a prior known accuracy.