Course Material

Course Structure

(13 weeks : 26 lectures/sessions) 

Part I : Left-Invariant Control Systems

Part II : Extension Techniques and Induced Systems

Part III : Controllability

Lectures/Sessions

(Left-invariant control systems)

WEEK 1 : Matrix Lie groups (and their Lie algebras)

WEEK 2 : Left-invariant vector fields

WEEK 3 : Left-invariant control systems

WEEK 4 : Orbits and reachable/attainable sets

WEEK 5 : Normal attainability

WEEK 6 : General controllability conditions

(Extension techniques and induced systems)

WEEK 7 : Saturate

WEEK 8 : Lie saturate of invariant system

WEEK 9 : Induced systems on homogeneous spaces

(Controllability)

WEEK 10 : Symmetric spaces. Compact Lie groups

WEEK 11 : Semisimple Lie groups

WEEK 12 : Solvable Lie groups

WEEK 13 : Semi-direct products of Lie groups