Geometric control theory

Back to my research page.

  1. Some open problems in geometric control theory.
    Reference: Fundamental problems of geometric control theory.
  2. Necessary and sufficient conditions for controllability of homogeneous systems.
    Reference: Small-time local controllability of homogeneous systems.
  3. A beautiful geometric formulation of stabilisation using linearisation.
    Reference: Geometric Jacobian linearization and LQR theory.
  4. A feedback-invariant formulation for control-affine systems, and a manner, using jet bundle geometry, for generating variations of trajectories.
    Reference: Jet bundles and algebro-geometric characterisations for controllability of affine systems.
  5. An example where the geometry of the system plays an interesting part in stabilisation.
    Reference: An example with interesting controllability and stabilisation properties.
  6. The geometry of Jacobian linearisation and controllability of linearisation along a trajectory.
    Reference: Jacobian linearisation in a geometric setting.
  7. Have you ever wondered what sliding mode control is? I did.
    Reference: Geometric sliding mode control: The linear and linearised theory.
  8. A method, based on the Campbell-Baker-Hausdorff formula, for generating a large class of control variations.
    Reference: Local controllability of families of vector fields.
  9. A general setting for control, and second-order controllability conditions within this framework.
    Reference: Geometric local controllability: second-order conditions.

Andrew D. Lewis (andrew at