Implicitly Modeled Control Systems

点击翻译按钮获取中文摘要

9500589 Campbell A differential algebraic equation (DAE) is an implicit ordinary differential equation. DAEs arise, for example, in a variety of control problems in flight control, robotics, chemical process control, and contact or constrained problems in mechanics. In addition, differential algebraic equations occur in the solution of partial differential equations by the method of lines and in many circuit models. DAEs are sometimes also called singular or descriptor systems. The last decade has seen considerable progress both in the analytical understanding of DAEs and in the development of numerical methods for DAEs. Most of this work has been in numerical analysis and has frequently involved complex nonlinear systems. Independently there has been considerable advancement in the development of theoretical results and methods for the control of nonlinear systems. With the exception of classical work based on time invariant linearizations most of this work in nonlinear control has dealt with comparatively smaller nonlinear systems. Many of this control development has been independent of the work on DAEs. As noted, many computer generated models are most naturally modeled in the form of DAEs. The move to the consideration of increasingly complex systems not only leads to DAE models but systems for which the more traditional nonlinear control methodologies are sometimes difficult to implement. This project will study implicity modeled control systems. The goal will not only be to extend existing techniques to the implicit setting but also to use the DAE technology from other areas such as numerical analysis to develop new and more efficient algorithms for computing control theoretic information from complex systems. ***