US-France Cooperative Research: Combinatorics in Nonlinear Systems Theory

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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.