Andrei Sarychev

Lie extensions and controllability results for nonlinear systems

1. Brief introduction into stability theory.

Basic definitions. Linearization principle.
Beyond the linearization principle: differential-geometric methods. Symmetric and nonsymmetric systems; orbit theorem

2. Extension of nonlinear control systems.

3. Convexification and introduction into theory of relaxed (sliding mode) controls.

4. Extensions beyond convexification: Lie saturation.

5. Nonlinear systems with generalized controls.

6. Extended (high-order) averaging and stability.

7. Lie extensions and controllability for some classes of PDE