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