Optimal Control on Lie Groups: The Projection Operator Approach

@article{Saccon2013OptimalCO,
  title={Optimal Control on Lie Groups: The Projection Operator Approach},
  author={Alessandro Saccon and John Hauser and Antonio Pedro Aguiar},
  journal={IEEE Transactions on Automatic Control},
  year={2013},
  volume={58},
  pages={2230-2245}
}
Many nonlinear systems of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. Examples range from aircraft and underwater vehicles to quantum mechanical systems. In this paper, we develop an algorithm for solving continuous-time optimal control problems for systems evolving on (noncompact) Lie groups. This algorithm generalizes the projection operator approach for trajectory optimization originally developed for systems on vector spaces. Notions for generalizing… CONTINUE READING
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