Implicitly Modeled Control Systems

9500589坎贝尔 微分代数方程（DAE）是一个隐式常微分方程。 例如，DAE出现在飞行控制、机器人、化学过程控制中的各种控制问题中，以及力学中的接触或约束问题中。 此外，微分代数方程出现在偏微分方程的解决方案，由线路的方法和许多电路模型。 DAE有时也称为奇异或描述符系统。 在过去的十年里，在对DAE的分析理解和DAE数值方法的发展方面都取得了相当大的进展。 大部分的工作一直在数值分析，并经常涉及复杂的非线性系统。 独立地，非线性系统控制的理论成果和方法的发展也取得了相当大的进展。 除了基于时不变线性化的经典工作之外，非线性控制中的大多数工作都处理相对较小的非线性系统。 这种控制开发中的许多工作都与DAE无关。 如前所述，许多计算机生成的模型最自然地以DAE的形式建模。 考虑日益复杂的系统不仅导致DAE模型，而且有时难以实施更传统的非线性控制方法的系统。 本计画将研究隐式模型化控制系统。 我们的目标将不仅是将现有的技术扩展到隐式设置，但也使用DAE技术从其他领域，如数值分析，开发新的和更有效的算法计算复杂系统的控制理论信息。 ***

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. ***