Implicitly Modeled Control Systems

9500589坎贝尔微分代数方程(DAE)是一种隐式常微分方程。例如，DAE出现在飞行控制、机器人、化学过程控制以及力学中的接触或约束问题中的各种控制问题中。此外，在用直线法求解偏微分方程组时，以及在许多电路模型中，都会出现微分代数方程。DAE有时也称为单系统或描述符系统。在过去的十年中，在对DAE的分析理解和发展DAE的数值方法方面都取得了长足的进步。这些工作大多是数值分析，经常涉及复杂的非线性系统。独立地讲，在非线性系统控制的理论结果和方法的发展方面已经有了相当大的进步。除了基于时间不变线性化的经典工作外，这些非线性控制方面的工作大多涉及相对较小的非线性系统。这些控制开发中的许多都独立于DAE上的工作。如上所述，许多计算机生成的模型最自然地以DAE的形式建模。转向考虑日益复杂的系统，不仅导致DAE模型，而且导致更传统的非线性控制方法有时难以实施的系统。本项目将研究隐式建模控制系统。目标不仅是将现有技术扩展到隐式设置，而且还将使用其他领域的DAE技术，如数值分析，以开发从复杂系统计算控制理论信息的新的、更有效的算法。***

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. ***