CDS/CIMMS Lunchtime Series: Stabilization and Synchronization of Networked Mechanical Systems

Dr. Sujit Nair, University of Southern California,
Dept of Mechanical and Aerospace Engineering

The main theme of this talk is coordination and stabilization of a network of  mechanical systems to achieve synchronized behaviour. Each individual system is a Lagrangian system with instabilities. The idea is to use kinetic and potential shaping to stabilize each individual system and to couple the systems    respectively. The resulting closed-loop system is also a Lagrangian system with a natural candidate for Lyapunov function. We build coordination techniques for two kinds of systems. The first one consists of underactuated Lagrangian systems with Abelian symmetry groups lacking gyroscopic forces. Next we consider rigid  body systems where the configuration space of each individual system is the non Abelian Lie group SO(3) or SE(3). Asymptotic stabilization is also considered  for all cases. The speaker will show why it is necessary to consider the problem of stabilization of individual systems and the problem of coupling the systems  for coordination purposes in an integrated manner.