Optimal feedback control, first-order PDE systems, and obstacle problems
Pablo Pedregal, Universidad de Castilla la Mancha (póster)
27 de septiembre. Aula 520, Departamento de Matemáticas, 12:00
Abstract. We will try to relate the three topics occurring in the title. By a suitable reformulation of a typical optimal control problem, one is led to consider the corresponding optimal feedback mapping as an equilibrium of such a reformulation. Hence, a typical descent algorithm may be used to approximate it. Each iteration of this procedure consists of two main steps: finding the solution (the costate) of a linear, first-order PDE system; and then, solving a typical obstacle problem. The result of this two-step process turns out to be a descent direction for the optimal feedback mapping of the problem. We will illustrate the performance of such an iterative scheme by testing it on several simple situations. The tone of the talk will be non-technical, so that only main ideas will be described in a way to make them understandable to a wide audience with a standard background in analysis.