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