Plenary Lecture

Regularity and Critical Cones in Optimal Control

Professor Javier F Rosenblueth
Applied Mathematics and Systems Research Institute
National Autonomous University of Mexico

Abstract: In this talk we explain how a well-known technique used to derive first and second order conditions for certain classes of constrained problems in optimization can be successfully generalized to optimal control theory. This method leads, in a natural way, necessary conditions on different critical cones according to different normality and regularity assumptions imposed on the corresponding extremals. We illustrate through some simple examples the usefulness of the conditions obtained in each case and introduce some recent applications of the main results on second order necessary and sufficient optimality conditions in calculus of variations and optimal control.

Brief Biography of the Speaker: Professor Rosenblueth holds a BSc in Mathematics from the National Autonomous University of Mexico and a PhD in Control Theory from the Imperial College of Science, Technology and Medicine, London, UK. He worked as a researcher in the Centre for Research in Mathematics, Guanajuato, Mexico and, since 1989, joined the Applied Mathematics and Systems Research Institute of the National Autonomous University of Mexico. He is Full Professor and currently a member of the Mathematical Physics Department. He has published more than 70 refereed papers, has spent sabbatical visits at the Weizmann Institute of Science, Rehovot, and Technion Israel Institute of Technology, Haifa, Israel, and has participated in numerous international conferences. His main research interests are in optimal control theory, variational analysis and optimization.

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