Information Theoretic Approaches To Model Reduction Of Dynamical Systems

The information theory and control theory have a tight connection. In recent years, there are more and more interactions between them. It is therefore no doubt that the information theory will offer us a new viewpoint for the analysis and design of the control system. The model reduction, a new branch of the modern control theory, has developed quickly in recent years, but the traditional model reduction methods didn't take the system information loss in charge.This dissertation mainly focuses on the information theoretic approaches to model reduction of dynamical systems. It can be divided into three parts: part one presents Shannon information theory and model reduction of dynamical systems; Part two puts forward a Revised Minimum Information Loss method for model reduction; Part three is the comparation between the Revised Minimum Information Loss method and traditional methods from the information viewpoint.The major contributions of this dissertation are stated as follows:1. It has purposed, in view of the problem that the reduced-order model generated by the Minimum Information Loss method is not unique, the Revised Minimum Information Loss method. The present method, by restricting the system to be the output normal model and therefore transforming the observability grammian to be an identity matrix, has minimized the total controllability and observability information loss and ensured the uniquness of the reduced-order model.2. It has compared, by analyzing the relation between the steady output information loss and the total controllability and observability information loss, the Revised Minimum Information Loss method with some other model reduction methods, such as Component Cost Analysis, q-COVER and Balanced Truncation Method.