Adaptive Control Of Uncertain Systems

The past decade has witnessed fast developments in the control theory of the nonlinear system. Especially, nonlinear systems with parameterized uncertainties attract more and more interest of people and become a focus of research. The studies and developments of uncertain parameterized nonlinear systems are of great importance for both theory and applications. There are two kinds of different uncertain parameters in the nonlinear systems: one is the linearized parameters, which enter the state equations linearly. Later, some efforts are made to remove such a linear parametrization requirement. That is the other one: the nonlinerized parameters, which are coupled nonlinearly with the measurable states. As far as the former's concerned, adaptive control or robust control is the general designing tool and the well-known one is the backstepping. This problem has been tackled easily. Two main methods can be adopted. The first one introduces a growth condition on the plant nonlinearties or a growth condition on a Lyapunov function. The second one imposes a canonical form for the system and restricitions on the parameter location. But for the nonlinear parameterization, there are very few reports in literature and it remains an open problem.In this thesis, the tracking problem of the nonlinear systems with uncertainties is studied, including both linearly parametrized uncertainties and nonlinearly parametrized uncertainties. The main results of this thesis are as follows:The first one is how to track the position accurately when parameters of the permanent magnet synchronous motor(PMSM) vary. Distinguishing from others, a canonical form is first introduced through a state transformation. Secondly, the control laws based on the backstepping method are designed to guarantee global stability and asymptotic tracking. A simulation result shows the controller has the advantages of rapid response, stability, no over-shoot etc. and arrives to the desired precision.The second one is about the tracking of nonlinear systems with nonlinear parameterization, including two parts. First, a tracking problem of nonlinear systems, in which all equations contain nonlinearized parameters and the control directions are...