# Geometric control theory

Back to my research page

- Some open problems in geometric control theory

**Reference:** *Fundamental problems of geometric control theory*
- Necessary and sufficient conditions for controllability of homogeneous
systems

**Reference:** *Small-time local controllability of homogeneous
systems*
- A beautiful geometric formulation of stabilisation using
linearisation

**Reference:** *Geometric Jacobian linearization and LQR
theory*
- 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*
- An example where the geometry of the system plays an interesting part in
stabilisation

**Reference:** *An example with interesting controllability and
stabilisation properties*
- The geometry of Jacobian linearisation and controllability of
linearisation along a trajectory

**Reference:** *Jacobian linearisation in a geometric
setting*
- Have you ever wondered what sliding mode control is? I did

**Reference:** *Geometric sliding mode control: The linear and
linearised theory*
- 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*
- 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 mast.queensu.ca)*