Accession Number : ADA311112

Title :   Research in Nonlinear Systems.

Descriptive Note : Final rept. 1 Sep 93-31 Aug 95,

Corporate Author : CORNELL UNIV ITHACA NY CENTER FOR APPLIED MATHEMATICS

Personal Author(s) : Holmes, Phillip

PDF Url : ADA311112

Report Date : 31 AUG 1995

Pagination or Media Count : 3

Abstract : There were no charges levied on this grant during the first year 9-1-93 to 8-31-94. The monies were used in academic year 1994-5 to support two PhD students, each in the final year of study and both working jointly with the PI on this grant, Philip Holmes, as well as John L. Lumley and Gal Berkooz. (The latter was Holmes PhD student, who graduated in 1991.) The students and their general research areas are as follows: Brianno Coller (Theoretical and Applied Mechanics): Control of nonlinear dynamical systems with heteroclinic cycles. The first paper on controlling heteroclinic cycles has appeared (1). A second paper (2), the text of an invited presentation at the Twelfth U.S. Congress on Applied Mechanics, appeared in mid 1994. In it we extend the methods for control of strongly nonlinear symmetric ODEs having heteroclinic cycles, developed earlier, to higher dimensional systems which provide more realistic models of the turbulent boundary layer. In Spring 1995 we completed a more extensive paper () in which we describe the use of optimal control theory in designing an algorithm to delay 'bursting' (transit of heteroclinic cycles) in a fairly general class of symmetric systems, which includes those appearing in low dimensional models of the turbulent boundary layer. In addition, Coller improved the analysis in (1) controlling vector fields and white noise perturbations.

Descriptors :   *NONLINEAR SYSTEMS, *CONTROL THEORY, ALGORITHMS, OPTIMIZATION, WHITE NOISE, TURBULENT BOUNDARY LAYER, SYMMETRY, VECTOR ANALYSIS, PERTURBATIONS, APPLIED MECHANICS.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE