Philip D. Loewen: Applications to Optimal Control

I will discuss the Generalized Problem of Bolza, in which a given integral functional is to be minimized over some subset of the class of absolutely continuous functions carrying the real interval [0,1] into a finite-dimensional Euclidean space. In the absence of differentiability, the classical Calculus of Variations provides guidance about the general appearance of results one should expect. However, the precise formulation of suitable nonsmooth extensions and the techniques required to prove them make essential use of recent developments in nonsmooth analysis. These lectures will treat, in varying levels of detail, problem formulation, necessary conditions for optimality, sufficient conditions for optimality, and optimal feedback control.