Location
Zoom (message amgrad@uwaterloo.ca for link)
Candidate
Thomas Newton | Applied Mathematics, University of Waterloo
Title
Optimal Actuator Design for PDE Control
Abstract
Control theory is concerned with making systems governed by differential equations behave in a desired manner. In optimal control, the goal is to design a controller—as a function of time or state—that minimizes a given cost. Often systems exhibit both spatial and temporal dynamics, and are modelled by partial differential equations (PDEs), which introduces additional challenges in ensuring well-posedness and in implementing effective control strategies numerically. A key consideration in PDE control is not only how the controller evolves over time, but also how it is distributed in space—leading to the problem of optimal actuator design. For example, in regulating room temperature, one must decide not only when and how much heat to apply but also where to place heaters; in vibration control of flexible structures, the placement or shape of actuators can significantly influence performance. This presentation introduces the setting for optimal actuator design in PDE control, reviews foundational work on the well-posedness of the problem and the existence of optimizers, then outlines open challenges in developing practical numerical routines, along with potential approaches to address them.