Thursday, May 7

Singularities of Solutions to Hamilton-Jacobi Equations with Applications to Optimal Control

8:00 AM-9:00 AM
Chair: Suzanne Lenhart, University of Tennessee, Knoxville
Room: Salon D

The dynamic programming approach to optimal control problems relies on the knowledge of the so-called value function, V, a nonsmmoth function that can be characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. The existence of a nondifferentiability set for V-- the singular set Sigma(V)--causes failure of most classical feedbacks. This fact motivated intensive research work that led to various generalized procedures for optimal synthesis. The speaker will outline the role of singular points in sufficient conditions for optimality. He will then present a survey of various results describing the structure of Sigma(V), providing rigorous estimates on the dimension of this set, and conclude by providing some insight into current trends of this theory, including extensions to infinite dimensional problems.

Piermarco Cannarsa
Dipartimento di Matematica, Universita di Roma "Tor Vergata," Italy

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MMD, 3/11/98