Optimal approach to shape parameter control

When describing the shape of a deformable object, two different approaches can be employed, referring either to local features or to global properties of the shape. Operating this choice influences both the modelling process of the system and the possibility of control- ling it. In this work we propose an approach to shape modelling and control based on parametric curves, rep- resenting the boundary of the object. The methodol- ogy proposed provides a compact representation of the shape by using a spline description of the curve, which at the same time shows interesting properties from the point of view of the control application. Moreover, integral parameters describing the shape as a whole (such as elongation, triangularity, squareness) find a suitable collocation in this framework, consistent with intuition and with the physics of the problem. The design of a controller for a specific application, namely the control of the plasma shape in fusion devices, is also presented. This example highlights the accuracy in the control capability of the spline controller and its completeness, in the sense that the control of the spline curve implies (but is not implied by) the control of shape local landmarks.