Free Access
Issue |
ESAIM: COCV
Volume 19, Number 4, October-December 2013
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Page(s) | 947 - 975 | |
DOI | https://doi.org/10.1051/cocv/2012040 | |
Published online | 04 July 2013 |
- R. Abraham and J.E. Marsden, Foundations of Mechanics, 2nd edition. Addison-Wesley (1978). [Google Scholar]
- R.M. Adams, R. Biggs and C.C. Remsing, Single-input control systems on the Euclidean group SE (2). Eur. J. Pure Appl. Math. 5 (2012) 1–15. [MathSciNet] [Google Scholar]
- A.A. Agrachev and Y.L. Sachkov, Control Theory from the Geometric Viewpoint. Springer-Verlag (2004). [Google Scholar]
- J.V. Armitage and W.F. Eberlein, Elliptic Functions. Cambridge University Press (2006). [Google Scholar]
- R. Biggs and C.C. Remsing, A category of control systems. An. Şt. Univ. Ovidius Constanţa 20 (2012) 355–368. [Google Scholar]
- R. Biggs and C.C. Remsing, On the equivalence of control systems on Lie groups. Publ. Math. Debrecen (submitted). [Google Scholar]
- R. Biggs and C.C. Remsing, On the equivalence of cost-extended control systems on Lie groups. Proc. 8th WSEAS Int. Conf. Dyn. Syst. Control. Porto, Portugal (2012) 60–65. [Google Scholar]
- R.W. Brockett, System theory on group manifolds and coset spaces. SIAM J. Control 10 (1972) 265–284. [CrossRef] [MathSciNet] [Google Scholar]
- D.D. Holm, J.E. Marsden, T. Ratiu and A. Weinstein, Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123 (1985) 1–116. [NASA ADS] [CrossRef] [Google Scholar]
- V. Jurdjevic, Non-Euclidean elastica. Amer. J. Math. 117 (1995) 93–124. [CrossRef] [MathSciNet] [Google Scholar]
- V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997). [Google Scholar]
- V. Jurdjevic, Optimal control problems on Lie groups: crossroads between geometry and mechanics, in Geometry of Feedback and Optimal Control, edited by B. Jakubczyk and W. Respondek, M. Dekker (1998) 257–303. [Google Scholar]
- V. Jurdjevic and H.J. Sussmann, Control systems on Lie groups. J. Differ. Equ. 12 (1972) 313–329. [Google Scholar]
- P.S. Krishnaprasad, Optimal control and Poisson reduction, Technical Research Report T.R.93–87. Inst. Systems Research, University of Maryland (1993). [Google Scholar]
- D.F. Lawden, Elliptic Functions and Applications. Springer-Verlag (1989). [Google Scholar]
- J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry. 2nd edition. Springer-Verlag (1999). [Google Scholar]
- I. Moiseev and Y.L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 380–399. [CrossRef] [EDP Sciences] [Google Scholar]
- J-P. Ortega and T.S. Ratiu, Non-linear stability of singular relative periodic orbits in Hamiltonian systems with symmetry. J. Geom. Phys. 32 (1999) 160–188. [CrossRef] [MathSciNet] [Google Scholar]
- J-P. Ortega, V. Planas-Bielsa and T.S. Ratiu, Asymptotic and Lyapunov stability of constrained and Poisson equilibria. J. Differ. Equ. 214 (2005) 92–127. [CrossRef] [Google Scholar]
- L. Perko, Differential Equations and Dynamical Systems, 3rd edition. Springer-Verlag (2001). [Google Scholar]
- M. Puta, Hamiltonian Mechanical Systems and Geometric Quantization. Kluwer (1993). [Google Scholar]
- M. Puta, S. Chirici and A. Voitecovici, An optimal control problem on the Lie group SE (2,R). Publ. Math. Debrecen 60 (2002) 15–22. [MathSciNet] [Google Scholar]
- M. Puta, G. Schwab and A. Voitecovici, Some remarks on an optimal control problem on the Lie group SE (2,R). An. Şt. Univ. A.I. Cuza Iaşi, ser. Mat. 49 (2003) 249–256. [Google Scholar]
- C.C. Remsing, Optimal control and Hamilton − Poisson formalism. Int. J. Pure Appl. Math. 59 (2010) 11–17. [Google Scholar]
- C.C. Remsing, Control and stability on the Euclidean group SE (2). Lect. Notes Eng. Comput. Sci. Proc. WCE 2011. London, UK, 225–230. [Google Scholar]
- Y.L. Sachkov, Maxwell strata in the Euler elastic problem. J. Dyn. Control Syst. 14 (2008) 169–234. [CrossRef] [MathSciNet] [Google Scholar]
- Y.L. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 1018–1039. [CrossRef] [EDP Sciences] [Google Scholar]
- Y.L. Sachkov, Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 17 (2011) 293–321. [CrossRef] [EDP Sciences] [Google Scholar]
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