Mathematics

PART 1: Controllability
-) Control systems: accessibility, controllability
-) Controllability of linear systems
-) Families of vector fields. Lie algebras
-) The Frobenious theorem
-) The orbit Theorem and the Krener theorem
-) Symmetric families: the Chow theorem
-) Compatible vector fields
-) Recurrent drift
-) Systems with unbounded controls

PART 2: Optimal control
-) Existence. The Filippov theorem
-) First order conditions. The Pontryagin Maximum Principle
-) Synthesis theory