# 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
theory*.
- 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
regularity.

**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
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)*