Geometric control theory
Back to my research page.
- 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
- A feedback-invariant framework for geometric control theory, using
topologies for spaces of vector fields and sheaf theory.
Reference: Tautological control systems.
- A unified topological framework for vector fields and flows of various
Reference: Time-varying vector fields and their flows.
- Some open problems in geometric control theory.
Reference: Fundamental problems of geometric control theory.
- Necessary and sufficient conditions for controllability of homogeneous
Reference: Small-time local controllability of homogeneous
- A beautiful geometric formulation of stabilisation using
Reference: Geometric Jacobian linearization and LQR
- A feedback-invariant formulation for control-affine systems, and a
manner, using jet bundle geometry, for generating variations of
Reference: Jet bundles and algebro-geometric
characterisations for controllability of affine systems.
- An example where the geometry of the system plays an interesting part in
Reference: An example with interesting controllability and
- The geometry of Jacobian linearisation and controllability of
linearisation along a trajectory.
Reference: Jacobian linearisation in a geometric
- Have you ever wondered what sliding mode control is? I did.
Reference: Geometric sliding mode control: The linear and
- A method, based on the Campbell-Baker-Hausdorff formula, for generating
a large class of control variations.
Reference: Local controllability of families of vector
- A general setting for control, and second-order controllability
conditions within this framework.
Reference: Geometric local controllability: second-order
Andrew D. Lewis (andrew at mast.queensu.ca)