Abstract : This research was concerned with analytical results related to control of distributed parameter systems. Existence of optimal controls was established for a variety of systems governed by partial differential equations, most of which involved boundary control. Much of the work also dealt nonlinearity. The work on switching systems promises to provide a theoretical baais for dealing under this grant, including A class of stabilizing feedback laws for marginally stable systems answers the question of how costly it is (in terms of control energy) to control quickly. Keywords: Reports; Abstracts.