Optimal control on SU(2) Lie group with stability analysis

Many configuration spaces of mechanical and non-mechanical problems in physical world involve matrix Lie groups. These Lie groups provide a mathematically rich formulation for studying a variety of control theory problems. While control systems have been specialized to different matrix Lie groups, study of optimal control of these systems by minimizing the input cost function has been a tempting research area. Here we take a left invariant driftless control system on the Lie group SU (2) and analyse controllability and optimal control of the system. Stability of the resulting dynamics from optimal control analysis is elaborated. Then numerical integration and some related properties are discussed via two unconventional integrators.