On the Controllability of Lagrangian Systems by Active Constraints

Open Access
Author:
Wang, Zipeng
Graduate Program:
Mathematics
Degree:
Master of Arts
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • Alberto Bressan, Thesis Advisor
Keywords:
  • Lagrangian
  • Constraints
  • Control
Abstract:
We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by implementing frictionless constraints. This leads to a system of ODE's whose right hand side depends quadratically on the time derivative of the control. In this paper we introduce a simplified dynamics, described by a differential inclusion. We prove that every trajectory of the differential inclusion can be uniformly approximated by a trajectory of the original system, on a sufficiently large time interval, starting at rest. Under a somewhat stronger assumption, we show this second trajectory reaches exactly the same terminal point.