LAUSR

The purpose of Optimal Control is to influence the behavior of a dynamical system in order to achieve a desired goal. Optimal control has a large variety of applications where the dynamics can be controlled optimally, such as aerospace, aeronautics, chemical plants, mechanical systems, finance and economics, but also to solve inverse problems where the goal is to determine input data in an equation from its solution values. An important application we will study in several settings is to determine the " data " in differential equations models using optimally controlled reconstructions of measured " solution " values. Inverse problems are typically harder to solve numerically than forward problems since they are often ill-posed (in contrast to forward problems), where ill-posed is the opposite of well-posed and a problem is defined to be well-posed if the following three properties holds (1) there is a solution, (2) the solution is unique, and (3) the solution depends continuously on the data. It is clear that a solution that does not depend continuously on its data is difficult to approximate accurately, since a tiny perturbation of the data (either as measurement error and/or as numerical approximation error) may 99