Control theory in classical mechanics. ***Provided position***

• Title: Control theory in classical mechanics.
• Location: Università Degli Studi di Padova, Italy
  
• Advisor: Franco Rampazzo
• Secondment: Imperial College London, UK
• Funding: 18 months.
• Contacts: Fabio Ancona; Franco Rampazzo
• Application deadline: June 30, 2011 or until position is filled.
• Key Words: holonomic and non holonomic constraints, nonlinear impulse systems, analysis and geometry of nonsmooth foliations
• Description of the subject:

In models where some coordinates are used as controls, the presence of quadratic terms in the derivatives of the controls is due to a curvature term of the foliation representing the moving constraint. In turn this quadratic term is responsible for interesting stabilization phenomena, exemplified by the inverted pendulum when the pivot is subject to rapid oscillations. Within this context, we wish first to investigate whether some kind of differential geometric classification of the involved foliations could help to simplify the theory. Secondly, in order to actually produce feedback stabilizing controls it should be helpful to analyze special kind of Hamilton-Jacobi inequalities. Finally, in the study of optimization problems, when the curvature term vanishes one ends up with a slow growth problem, which is particularly interesting because of the presence of non vanishing Lie brackets. In perspective, the addition of non holonomic constraints to the mechanical system will be a source of new geometric and analytic issues.

The fellowship is composed of 12 months research at Università Degli Studi di Padova and 6 months at Imperial College London

Requirements: PhD Degree. Interest in control theory and/or mechanics. Some knowledge in ordinary differential equations and 1st order partial differential equations.