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Publications

Papers

Forthcoming

  • R Biggs, CC Remsing, Invariant control systems on Lie groups. In: G. Falcone (ed.), Lie Groups, Differential Equations, and Geometry: Advances and Surveys, Springer.

2017

  • R Biggs, CC Remsing, Quadratic Hamilton–Poisson systems in three dimensions: equivalence, stability, and integration. Acta Appl. Math. 148(2017), 1–59. [DOI] [Online PDF] [RG]
  • CE Bartlett, R Biggs, CC Remsing, A few remarks on quadratic Hamilton-Poisson systems on the Heisenberg Lie-Poisson space. Acta Math. Univ. Comenianae. 86(1)(2017), 73–79.  [Link] [RG]

2016

  • RM Adams, R Biggs, W Holderbaum, CC Remsing, Stability and integration of Hamilton-Poisson systems on so(3)*.  Rend. Mat. Appl. 37(2016), 1–42.  [Link] [RG]
  • R Biggs, CC Remsing, Equivalence of control systems on the pseudo-orthogonal group SO(2,1). An. Stiint. Univ. Ovidius Constanta. 24(2)(2016), 45–65.  [DOI] [RG]
  • DI Barrett, R Biggs, CC Remsing, O Rossi, Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. J. Geom. Mech. 8(2)(2016), 139–167.  [DOI] [RG]
  • R Biggs, PT Nagy, On sub-Riemannian and Riemannian structures on the Heisenberg groups. J. Dyn. Control Syst. 22(2016), 563–594.  [DOI] [RG]
  • R Biggs, CC Remsing, On the classification of real four-dimensional Lie groups. J. Lie Theory. 26(2016), 1001–1035.   [Link] [RG]
  • R Biggs, PT Nagy, On extensions of sub-Riemannian structures on Lie groups. Differential Geom. Appl. 46(2016), 25–38.   [DOI] [RG]
  • MA Henning, V Naicker, Bounds on the disjunctive total domination number of a tree. Discuss. Math. Graph Theory 36(2016), 153–171.  [DOI]
  • MA Henning, V Naicker, Disjunctive total domination in graphs. J. Comb. Optim. 31(3)(2016), 1090–1110.  [DOI] [arXiv]
  • CE Bartlett, R Biggs, CC Remsing, Control systems on the Heisenberg group: equivalence and classification. Publ. Math. Debrecen 88(1-2)(2016), 217–234.  [Link] [RG]

2015

  • DI Barrett, R Biggs, CC Remsing, Affine distributions on a four-dimensional extension of the semi-Euclidean group. Note Mat. 35(2)(2015), 81–97.   [DOI] [RG]
  • R Biggs, CC RemsingOn the equivalence of control systems on Lie groupsCommun. Math. 23(2)(2015), 119–129.  [Link] [RG]
  • MA Henning, V Naicker, Graphs with large disjunctive total domination. DMTCS 17(1)(2015), 255–282. [Link] [arXiv]
  • R  Biggs, CC Remsing, Subspaces of the real four-dimensional Lie algebras: a classification of subalgebras, ideals, and full-rank subspaces. Extracta Math. 31(1)(2015), 41–93.  [Link] [RG]
  • DI Barrett, R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems on se(1,1)*: the homogeneous case. Int. J. Geom. Methods Mod. Phys. 12(2015), 1550011 (17 pages).  [DOI] [RG]

2014

  • R Biggs, CC Remsing, Some remarks on the oscillator group. Differential Geom. Appl. 35(2014), 199–209.  [DOI] [RG]
  • R Biggs, CC Remsing, Control systems on three-dimensional Lie groups: equivalence and controllability. J. Dyn. Control Syst. 20(3)(2014), 307–339.  [DOI]  [RG]
  • DI Barrett, R Biggs, CC Remsing, Affine subspaces of the Lie algebra se(1,1). Eur. J. Pure Appl. Math. 7(2)(2014), 140–155.   [Link] [RG]
  • R Biggs, CC Remsing, Cost-extended control systems on Lie groups. Mediterr. J. Math. 11(1)(2014), 193–215.  [DOI] [RG]

2013

  • R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, II. Note Mat. 33(2)(2013), 19–31.   [DOI] [RG]
  • RM Adams, R Biggs, CC Remsing, Control systems on the orthogonal group SO(4). Commun. Math. 21(2)(2013), 107–128.   [Link] [RG]
  • R Biggs, PT Nagy, A classification of sub-Riemannian structures on the Heisenberg groups. Acta Polytech. Hungar. 10(7)(2013), 41–52.  [DOI] [RG]
  • R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, I.  Arch. Math. (Brno) 49(3)(2013), 187–197.  [DOI] [RG]
  • RM Adams, R Biggs, CC Remsing, Two-input control systems on the Euclidean group SE(2). ESAIM: Control Optim. Calc. Var. 19(4)(2013), 947–975.  [DOI] [RG] 
  • R Biggs, CC Remsing, Control affine systems on semisimple three-dimensional Lie groups. An. Stiint. Univ. "A.I. Cuza" Iasi Mat. 59(2)(2013), 399–414.  [DOI] [RG]
  • RM Adams, R Biggs, CC Remsing, On some quadratic Hamilton-Poisson systems. Appl. Sci. 15(2013), 1–12.  [Link] [RG]

2012

  • R Biggs, CC Remsing, A note on the affine subspaces of three-dimensional Lie algebras. Bul. Acad. Stiinte Repub. Mold. Mat. 2012, no.3, 45–52.  [Link] [RG]
  • RM Adams, R Biggs, CC Remsing, Equivalence of control systems on the Euclidean group SE(2). Control Cybernet. 41(3)(2012), 513–524.  [Link] [RG]
  • CC Remsing, Optimal control on the rotation group SO(3). Carpathian J. Math. 28(2)(2012), 305–312.  [PDF] [RG]
  • R Biggs, CC Remsing, A category of control systems. An. St. Univ. Ovidius Constanta 20(1)(2012), 355–368.  [DOI] [RG]
  • 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.  [Link] [RG]

2011

  • CC Remsing, Optimal control and integrability on Lie groupsAn. Univ. Vest. Timis. Ser. Mat.-Inform. 49(2)(2011), 101–118.   [Link] [RG]

2010

  • CC Remsing, Optimal control and Hamilton-Poisson formalism. Int. J. Pure. Appl. Math. 59(1)(2010), 11–17.  [Link] [RG]

Conference proceedings

2014

  • DI Barrett, R Biggs, CC Remsing, Optimal control of drift-free invariant control systems on the group of motions of the Minkowski plane. Proc. 13th European Control Conference, Strasbourg, France, 2466–2471.  [DOI] [RG]
  • R Biggs, CC Remsing, Control systems on three-dimensional Lie groups. Proc. 13th European Control Conference, Strasbourg, France, 2442–2447.  [DOI] [RG]

2013

  • RM Adams, R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems on so(3)*: classification and integration. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 55–66.  [RG]
  • R Biggs, CC Remsing, A classification of quadratic Hamilton-Poisson systems in three dimensions. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 67–78.  [RG]
  • R Biggs, CC Remsing, Feedback classification of invariant control systems on three-dimensional Lie groups. Proc. 9th IFAC Symp. Nonlinear Control Syst., Toulouse, France, 506–511.  [PDF] [RG]

2012

  • 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, 60-65.  [PDF] [RG]
  • 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, 54–59.  [PDF] [RG]

2011

  • CC Remsing, Control and stability on the Euclidean group SE(2). Lect. Notes Eng. Comp. Sci.: Proc. WCE 2011, London, UK, 225–230.  [PDF] [RG]

2010

  • CC Remsing, Integrability and optimal control. Proc. MTNS 2010, Budapest, Hungary, 1749–1754.  [PDF] [RG]
  • CC Remsing, Control and integrability on SO(3). Lect. Notes. Eng. Comp. Sci.: Proc. WCE 2010, London, UK, 1705–1710.  [PDF] [RG]

Preprints 

  • DI Barrett, CC Remsing, A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups.
  • CE Bartlett, R Biggs, CC Remsing, Control systems on nilpotent Lie groups of dimension ≤ 4: equivalence and classification.
  • R Biggs, Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups.
  • R Biggs, G Falcone, A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms.
  • DI Barrett, R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems on se(1,1)*: the inhomogeneous case.
  • R Biggs, CC Remsing, Invariant control systems on Lie groups: a short survey of some recent results.

  

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