Observer Design For One-sided Lipschitz Nonlinear Systems And Its Application In Mechanical Systems

Knowing the state of a dynamical system plays a key role in the solution of many problems such as stabilization and decoupling problems that arise in control theory and industrial automation. However, in some situations it is not easy to directly obtain state through sensors or it is impossible to gain all the state variables due to the restrictions in economics or physics. Generally, under these circumstances, we need construct a state observer which provides reconstructed state estimate based on the available input-output information of systems. Then, we use the estimated state to replace the real state to impose the state feedback. Therefore, the state estimation or observer design problems are very important not only in the theoretical study but also in many engineering practices. In fact, state observer has many applications in disturbance estimation, observer-based fault diagnosis and isolation, chaotic synchronization etc.In practice many physical systems, a great many mechanical control systems are included, are essentially nonlinear and even singular. Observer design for linear time-invariant systems is well understood but the more important nonlinear observer design problem continues to be a challenge and no universal solution has been found. Therefore, the state estimation problem for nonlinear singular systems is very important and deserves to further study. In the existing literature, Lipschitz condition is a commonly used assumption in the observer design. This is partly due to the fact that many physical systems satisfy this condition. However, most of the available observer designs for Lipschitz nonlinear systems only work for systems with small small Lipschitz constants but often fail to provide a solution when the Lipschitz constants become large. To overcome this limitation, in this thesis we introduce the one-sided Lipschitz condition, which contains the classical Lipschitz condition as a special case. Moverover, in the observer design we take model uncertainties and unknown disturbances into account and propose new design methods for one-sided Lipschitz singular nonlinear systems. Both full-order and reduced-order observers are considered and the applications in the control design of one-link flexible manipulator are also addressed.The thesis is divided into 6 chapters. The main contributions can be summarized as follows:(1) With the help of Lyapunov stability theory and H? observer design method, we address the observer design problem for continuous-time Lipschitz descriptor nonlinear systems in the presence of disturbances and model uncertainties. The problem has been transferred into solving a set of linear matrix inequalities, which can be easily solved via numerical software such as Matlab LMI tools.(2) Under the framework of one-sided Lipschitz setting, we consider the full-order and reduced-order observer designs for discrete-time descriptor nonlinear systems. Compared to some existing results, the proposed results are less conservative and can work for systems with a larger Lipschitz constant. The applications of the proposed observer design in mechanical systems are also considered.(3) We design an observer-based output feedback controller for one-sided Lipschitz nonlinear systems. Sufficient conditions that guarantee the existence of observer-based output feedback are established in the form of linear matrix inequalities, which are readily solved by the available numerical software. Moreover, the proposed observer-based output feedback designs are applied to a flexible link manipulator system. The efficiency of the proposed full-order and reduced-order observers and the observerbased output feedback controller are illustrated by means of Scilab and Matlab platforms. The simulation results are well verified the main conclusions of the thesis.