Robust Adaptive Control Of Uncertain General Lower-Triangular Nonlinear Systems And Its Application In Power Systems

The research of nonlinear systems has been the focus of attention in the field of control since the control objects are inherently nonlinear. The modern nonlinear science discovers a lot of facts, which show that the nonlinear cases are so complicated that they are neither characterized by linear system theory, nor modelled by the exact functions. Moreover, it is difficult to find an effective method to deal with all kinds of nonlinear systems. To overcome the hurdle, the investigators proposed a few techniques to handle some types of nonlinear systems, which make considerable progress in analyzing and designing nonlinear systems.The lower-triangular nonlinear system is a class of important models in the field of nonlinearity. The name of it comes from the lower-triangular form of system matrix in state-space equations when it is linear. For nonlinear case, the lower-triangular structure has the step-up relations between the states in the nonlinear differential equations, which are helpful to design the controller for the class of systems. Owing to the character of structure of lower-triangular system, the high-rank state of each differential equation is used as virtual control, then the control law is constructed by recursive design. The research about the low-triangular system is not only important theoretically but also significant practically. Many systems for application either conform to the form or are possible to be transformed into this form. Among the previous work, the well-known representations of lower-triangular system are strict-feedback system and high-order lower-triangular system.On the other hand, the uncertainties exist in all physical systems, which come from modelling simplifications, modelling error, external disturbances and measurement noise. The uncertain parts are classified into static uncertainties and dynamic uncertainties. Static uncertainties consist of unknown parameters, unknown disturbances and unknown nonlinear functions; and dynamic uncertainties come from the ignored dynamic character and slowly-varying parts in the models, the dynamic actions which result from the nonlinear factors appearing at the system input. How to deal with these uncertainties is one difficult problem in the field of control, which have to be solved for the application of nonlinear design methods.In this dissertation, polynomial lower-triangular system and general lower-triangular system are bringed forward, which extend the triangular system to more general case. Moreover, we investigate the design method of uncertain lower-triangular systems, which include static uncertainties and dynamic uncertainties. In the end, the obtained design idea and control law are applied to power systems to solve the control problems of electrical machines.In our thesis, contents are organized as follows:In Chapter 1, we introduce the background of this topic, internal and overseas research situations, theoretical and practical significance, and present the research objects and the main contributions of this dissertation.Chapter 2 reviews the development of the stability results for nonlinear systems and some relevant theories, which include main Lyapunov theorem and LaSalle invariance theorem, the definition of input-output stability; control Lyapunov function and Sontag's formula, Lyapunov redesign method; the conceptions of passivity and dissipation, pas-...