Research interests: geometric control theory; sub-Riemannian geometry; Lie theory
Theme 1: Invariant optimal control problems on matrix Lie groups
- Pontryagin maximum principle (PMP)
- Lie-Poisson formalism
- Normal and abnormal extremals
- Geometry of extremals
- Integrability
- Explicit integration (by elliptic functions)
- Stability (via energy-Casimir method)
- Periodic orbits
Theme 2: Categories of control systems, equivalences
- Left-invariant control systems
- Left-invariant control affine systems
- Cost-extended (left-invariant) control systems
- Controllability
- State space equivalence (S-equivalence)
- (Detached) feedback equivalence (DF-equivalence)
- L-equivalence, A-equivalence
- C-equivalence
Theme 3: Sub-Riemannian geometry (and optimal control)
- Geodesics
- Curvature of distributions/control systems
- Optimal control on the (3D) Heisenberg group
- Optimal control on the (4D) oscillator group
- (Left-invariant) SR structures
- Local equivalence of (left-invariant) SR structures
- Left-invariant SR structures on 3D Lie groups
- Left-invariant SR structures on 4D Lie groups
Theme 4: Poisson structures (and optimal control)
- Poisson algebras
- Quadratic Poisson structures
- Lie-Poisson structures and Casimir invariants
Last Modified: Tue, 11 Sep 2012 12:02:07 SAST
