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