Geometry and Geometric Control Research Group (GGC)

Coordinator : CC Remsing

Members

• RM Adams
• R Biggs
• DI Barrett
• CE Bartlett

Former members

• HC Henninger (2010-2011)

Topics

• Categories of (invariant) control systems, equivalences, classification
• Invariant optimal control problems on (matrix) Lie groups
• Poisson structures (and optimal control)
• Curvature of control systems
• Sub-Riemannian geometry (and optimal control)
• Sub-Lorentzian geometry (and optimal control)
• Integrability of Hamiltonian systems on Lie algebras (and optimal control)
• Stability of Hamiltonian systems on Lie algebras (and optimal control)

Publications

Preprints

• (R Biggs, CC Remsing) Optimal control on the Heisenberg group: equivalence and integration.

• (DI Barrett, R Biggs , CC Remsing) Quadratic Hamilton-Poisson systems on se(1,1)*_: the homogeneous case.

• (R Biggs, CC Remsing) Feedback classification of invariant control systems on three-dimensional Lie groups.

• (R Biggs, CC Remsing) Control systems on three-dimensional Lie groups: equivalence and controllability.
• (DI Barrett, R Biggs, CC Remsing) Affine subspaces of the Lie algebra se(1,1).

• (RM Adams, R Biggs, CC Remsing) Control systems on the orthogonal group SO(4).

• (R Biggs, CC Remsing) Cost-extended control systems on Lie groups.

• (R Biggs, CC Remsing) Equivalence of control systems on the pseudo-orthogonal group SO(2,1).
• (R Biggs, CC Remsing) Control affine systems on solvable three-dimensional Lie groups, I.
• (R Biggs, CC Remsing) A note on the affine subspaces of three-dimensional Lie algebras.
• (R Biggs, CC Remsing) On the equivalence of control systems on Lie groups.

Published papers

• (RM Adams, R Biggs, CC Remsing) On some quadratic Hamilton-Poisson systems. Appl. Sci. 15(2013) (to appear)
• (R Biggs, CC Remsing) Control affine systems on solvable three-dimensional Lie groups, II. Note Mat. 33(2013) (to appear)

• (R Biggs, CC Remsing) Control affine systems on semisimple three-dimensional Lie groups. An. St. Univ. "A.I. Cuza" Iasi Ser. Mat. 59(2013) (to appear)
• (RM Adams, R Biggs, CC Remsing) Equivalence of control systems on the Euclidean group SE(2). Control Cybernet. 41(3)(2012), 513-524.
• (RM Adams, R Biggs, CC Remsing) Two-input control systems on the Euclidean group SE(2). ESAIM Control Optim. Calc. Var. 19(2013) (to appear)
• (CC Remsing) Optimal control on the rotation group SO(3). Carpathian J. Math. 28(2)(2012), 305-312.
• (R Biggs, CC Remsing) A category of control systems. An. St. Univ. Ovidius Constanta 20(1)(2012), 355-368.
• (RM Adams, R Biggs, CC Remsing) Single-input control systems on the Euclidean group SE(2). Eur. J. Pure Appl. Math. 5(1)(2012), 1-15.

• (CC Remsing) Optimal control and integrability on Lie groups. An. Univ. Vest. Timis. Ser. Mat.-Inform. 49(2)(2011), 101-118.

• (CC Remsing) Optimal control and Hamilton-Poisson formalism. Int. J. Pure. Appl. Math. 59(1)(2010), 11-17.
• (CC Remsing) Note on an explicit isomorphism. An. Univ. Vest Timis. Ser. Mat.-Inform. 44(2)(2006), 135-141.

Proceedings to conferences

• (R Biggs, CC Remsing) On the equivalence of cost-extended control systems on Lie groups. Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal (2012), 60-65.
• (RM Adams, R Biggs, CC Remsing) On the equivalence of control systems on the orthogonal group SO(4). Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal (2012), 54-59

• (CC Remsing) Control and stability on the Euclidean group SE(2). Lect. Notes Eng. Comp. Sci.: Proc. WCE 2011, London, UK, pp. 225-230.
• (CC Remsing) Integrability and optimal control. Proc. MTNS 2010, Budapest, Hungary, pp. 1749-1754.
• (CC Remsing) Control and integrability on SO(3). Lect. Notes. Eng. Comp. Sci.: Proc. WCE 2010, London, UK, pp. 1705-1710.

Talks, presentations, reports, etc.

• (CE Bartlett) The geometry of the Heisenberg group H_3. Maths Seminar, Rhodes Univ, 2012 (Honours project).
• (CE Bartlett) Hamilton-Poisson formalism and geometric control on Lie groups. Maths Seminar, Rhodes Univ, 2012 (Honours project).

• (DI Barrett) A classification of control systems on SE(1,1). Maths Seminar, Rhodes Univ, 2012 (MSc report).

• (RM Adams) On the equivalence of control systems on the orthogonal group SO(4). CONTROL 2012, Porto (Portugal). 
• (R Biggs) On the equivalence of cost-extended control systems on Lie groups. CONTROL 2012, Porto (Portugal).

• (R Biggs) Cost-extended control systems. Maths Seminar, Rhodes Univ, 2012 (PhD report).

• (HC Henninger) Controllability of left-invariant control affine systems on the Lorentz group SO(1,2). Joint Meeting SAMS-AMS, Port Elizabeth, 2011.
• (R Biggs) On the equivalence of control systems on Lie groups. Joint Meeting SAMS-AMS, Port Elizabeth, 2011.
• (RM Adams) Equivalence of control systems on the Euclidean group SE(2). Joint Meeting SAMS-AMS, Port Elizabeth, 2011.
• (DI Barrett) The semi-Euclidean group SE(1,1). Maths Seminar, Rhodes Univ, 2011 (Honours project).
• (DI Barrett) The Campbell-Baker-Hausdorff theorem. Maths Seminar, Rhodes Univ, 2011 (Honours project).
• (RM Adams) Elliptic functions and optimal control. Maths Seminar, Rhodes Univ, 2011 (PhD report).
• (HC Henninger) Controllability on the Lorentz group. Maths Seminar, Rhodes Univ, 2011 (MSc report).
• (R Biggs) Control systems on the oscillator group. Maths Seminar, Rhodes Univ, 2011 (MSc report).
• (CC Remsing) Control and stability on the Euclidean group SE(2). ICAEM 2011, London (UK).
• (CC Remsing) An optimal control problem on the Euclidean group SE(2). ICAAA 2011, Istanbul (Turkey).
• (R Biggs) The category of left-invariant control systems. Maths Seminar, Rhodes Univ, 2010 (MSc report).
• (HC Henninger) Hyperbolic geometry on geometric surfaces. Maths Seminar, Rhodes Univ, 2010 (MSc report).
• (RM Adams) The Euclidean group SE(2). Maths Seminar, Rhodes Univ, 2010 (MSc report).
• (CC Remsing) Control and integrability on SO(3). ICAEM 2010, London (UK).
• (CC Remsing) Integrability and optimal control. MTNS 2010, Budapest (Hungary).
• (CC Remsing) Stability and optimal control. ICMS 2009, Istanbul (Turkey).
• (CC Remsing) Optimal control, stability, and Hamilton-Poisson formalism. ICAMC 2008, Plovdiv (Bulgaria).
• (CC Remsing) Matrix Lie groups. Maths Seminar, Rhodes Univ, 2007.