Controlling Curves on the Plane: An Approach to Shape Control in Fusion Devices

The shaping and more in general the control of the shape of a deformable object is a challenging task, because of the intrinsic infinite-dimensionality of the controlled object. This issue can be faced by adopting a suitable description of the frontier of the object, which also drives the design of the controller. In this work we explore the possibility of using two-dimensional curves to represent and control shapes subject to continuous deformation. Firstly, we state the problem from a formal point of view and we present an interesting application, the shape control in nuclear fusion devices. Then, we proceed with setting some guidelines for the design of integral controllers based on the contour representation and synthesize an optimal regulator for the specific application. Remarkably, this approach represents a novel paradigm in shape control, in that it gives the role of controlled variables to a collection of shape parameters instead of using samples from the boundary. The control action benefits from this as the object appears to follow the deformation more consistently