Plenary Lecture

Weak and Strong Normality in Optimal Control

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

Abstract: In theorems on first order necessary conditions in optimal control theory, a weak notion of normality is usually assumed in order to guarantee the non-vanishing of the cost multiplier. However, for problems involving inequality and equality constraints in the control functions, this notion is not enough to ensure the validity of second order necessary conditions and a stronger one is needed. In some references, this stronger notion takes into account only equality constraints for active indices and, in doing so, the set of critical directions may become too restrictive. In this talk we explain how, for certain classes of optimal control problems, not only that set of directions can be enlarged but also the normality assumptions can be weakened. As we shall see, these new results may play a fundamental role in finding solutions to the optimal control problem.

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 75 refereed papers, has spent sabbatical visits at the Weizmann Institute of Science, Rehovot, and Technion Israel Institute of Technology, Haifa, Israel, is associate editor of several refereed journals, and has participated in numerous international conferences. His main research interests are in optimal control theory, calculus of variations, variational analysis and optimization.

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