Geometric control theory

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  1. A new way of viewing control systems, using topologies for spaces of vector fields. This allows, for example, a coherent formulation for real analytic control systems.
    Reference: Locally convex topologies and control theory.
  2. A feedback-invariant framework for geometric control theory, using topologies for spaces of vector fields and sheaf theory.
    Reference: Tautological control systems.
  3. A unified topological framework for vector fields and flows of various regularity.
    Reference: Time-varying vector fields and their flows.
  4. Some open problems in geometric control theory.
    Reference: Fundamental problems of geometric control theory.
  5. Necessary and sufficient conditions for controllability of homogeneous systems.
    Reference: Small-time local controllability of homogeneous systems.
  6. A beautiful geometric formulation of stabilisation using linearisation.
    Reference: Geometric Jacobian linearization and LQR theory.
  7. 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.
  8. An example where the geometry of the system plays an interesting part in stabilisation.
    Reference: An example with interesting controllability and stabilisation properties.
  9. The geometry of Jacobian linearisation and controllability of linearisation along a trajectory.
    Reference: Jacobian linearisation in a geometric setting.
  10. Have you ever wondered what sliding mode control is? I did.
    Reference: Geometric sliding mode control: The linear and linearised theory.
  11. 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.
  12. 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