US-France Cooperative Research: Combinatorics in Nonlinear Systems Theory

该奖项将支持系统理论的合作研究 彼得克劳奇博士，亚利桑那州立大学和博士。 Francoise Lamnabhi-Lagarrigue，信号和系统公司， 法国伊维特河畔吉夫的电力学院。 的 该项目的目标是开发高效的 非线性控制系统的计算算法 代数和组合算法。 拟议研究的科学效益来自于 事实上，与线性系统的情况不同，电流 非线性控制系统的新理论尚未发展 这足以使它们被工业界广泛接受。 现代控制技术的设计者。 线性理论现在 发展到计算机不仅被用作工具的阶段 实现控制算法作为一个组成部分， 物理工厂，而且在算法的自动化设计。 相反，在非线性系统的情况下， 设计问题是这样的，即使有时它是 可能证明解决方案的存在性，通常不可能。 可以以计算的方式制定解决方案， 可实施的。 该项目旨在解决这些问题。 问题通过使用数学和数值技术 符号计算。 这个项目的成功 将是很大的帮助，在设计控制器， 复杂系统，如机器人、空间站和飞机。 的 项目将受益于两个互补的专业知识 非线性系统理论的研究者及其过去的历史 成功的合作。

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.