US-France Cooperative Research: Combinatorics in Nonlinear Systems Theory

该奖项将支持亚利桑那州立大学的Peter Crouch博士和法国Gif-sur-Yvette的Ecole Superieure d‘Electricite实验室的Francoise Lamnabhi-Lagarrigue博士在系统理论方面的合作研究。该项目的目标是利用代数和组合算法开发用于非线性控制系统的有效计算算法。这项研究的科学意义在于，与线性系统的情况不同，目前的非线性控制系统的新理论还没有得到充分的发展，不足以被现代控制技术的工业设计师广泛接受。线性理论现在已经发展到这样一个阶段，在这个阶段，计算机不仅被用作实现控制算法的工具，作为物理对象的一个组成部分，而且还被用于算法的自动化设计。相反，在非线性系统的情况下，设计问题的复杂性是这样的，即使有时可能证明解的存在，但通常不可能以可计算实现的方式来表示解。该项目旨在通过使用数学和数字技术以及符号计算来解决这些问题。该项目的成功成果将对机器人、空间站和飞机等复杂系统的控制器设计有很大帮助。该项目将受益于两位研究人员在非线性系统理论方面的互补专业知识和他们过去成功合作的历史。

This award will support collaborative research in systems theory between Dr. Peter Crouch, Arizona State University and Dr. Francoise Lamnabhi-Lagarrigue, Laboratoire de Signaux et Systemes, Ecole Superieure d'Electricite, Gif-sur-Yvette, France. The objective of the proposed project is the development of efficient computational algorithms for nonlinear control systems using algebraic and combinatorial algorithms. The scientific benefit of the proposed research arises from the fact that, unlike the situation for linear systems, the current new theories for nonlinear control systems have not yet developed sufficiently for their widespread acceptance by the industrial designers of modern control technology. The linear theory is now developed to a stage where the computer is used not only as a tool to implement control algorithms as an integral part of the physical plant, but also in the automated design of the algorithms. Conversely, in the case of nonlinear systems, the complexity of the design problems are such that, even though sometime it is possible to prove the existence of solutions, it is usually not possible to formulate the solutions in a manner that is computa- tionally implementable. This project is aimed at addressing these issues through the use of mathematical and numerical techniques and symbolic computation. The successful outcome of this project will be of great assistance in the design of controllers for complex systems, such as robots, space stations and aircraft. The project will benefit from the complementary expertise of the two investigators in nonlinear systems theory and their past history of successful collaboration.