The Application Of State Observer For Lipschitz Nonlinear System To Inverse System Method

With the development of nonlinear control theory, especially feedback linearization, nonlinear state observer design and nonlinear system control based on state observer are becoming more and more important. In the process of applying the inverse system method to feedback linearization, the inverse system requires the feedback of the whole state. In practice, however, all state variables are rarely available from online measurement due to either the difficulties of measuring state directly or the economic and utilizing limitations of measuring equipment. This makes state feedback can not be physically realized. The fact that the function of the state feedback can not be replaced and the physical realization for state feedback can not be reached makes up a kind of contradiction. Based on the properties that the system can use the inverse system method, this paper applies the state observer design of Lipschitz nonlinear system to the inverse system method, which can reconstruct the state variables of the system and use it to replace the actual state variables of the system to satisfy the whole state feedback. The main contents of this paper are composed of the following four parts:1. In this part, through analyzing and studying the predecessors'observer design theory of Lipschitz nonlinear system, the design method that is applied to the inverse system method is put forward. This method proposes the sufficient conditions on existence of nonlinear state observer. Furthermore, analytic solutions on observer gain are given by linear matrix inequality of MATLAB, which can greatly reduce the counted amount.2. In this part, based on the properties that the system can use the inverse system method, the feasibility that the observer design of Lipschitz nonlinear system is applied to the inverse system method is proposed. Furthermore, application of this kind of observer for the inverse system method is put forward by two respects of single variable and multi variables.3. In this part, aiming at the application of observer for the inverse system method in multi variables system, simulation is carried out with the actual chemical model (FCCU reproducibility model).4. As an expansion, for a class of nonlinear system with parameter uncertainty, this part makes the fundamental research to the observer design and proposes the sufficient conditions on existence of nonlinear state observer. Furthermore, analytic solutions on observer gain are given.