- J.T. Betts, Survey of numerical methods for trajectory optimization. Journal of Guidance, Control and Dynamics 21 (1998) 193–207.
- W.M. Boothby, An introduction to Differential Geometry and Riemannian Manifolds. Academic Press (1975).
- P. Crouch, M. Camarinha and F. Silva Leite, Hamiltonian approach for a second order variational problem on a Riemannian manifold, in Proc. of CONTROLO'98, 3rd Portuguese Conference on Automatic Control (September 1998) 321–326.
- P. Crouch, F. Silva Leite and M. Camarinha, Hamiltonian structure of generalized cubic polynomials, in Proc. of the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (2000) 13–18.
- P. Crouch, F. Silva Liete and M. Camarinha, A second order Riemannian varational problem from a Hamiltonian perspective. Private Communication (2001).
- T. Frankel, The Geometry of Physics: An Introduction. Cambridge University Press (1998).
- R. Holsapple, R. Venkataraman and D. Doman, A modified simple shooting method for solving two point boundary value problems, in Proc. of the IEEE Aerospace Conference, Big Sky, MT (March 2003).
- R. Holsapple, R. Venkataraman and D. Doman, A new, fast numerical method for solving two-point boundary value problems. J. Guidance Control Dyn. 27 (2004) 301–303. [CrossRef]
- V. Jurdejevic, Geometric Control Theory. Cambridge Studies in Advanced Mathematics (1997).
- P.S. Krishnaprasad, Optimal control and Poisson reduction. TR 93–87, Institute for Systems Research, University of Maryland, (1993).
- A. Lewis, The geometry of the maximum principle for affine connection control systems. Preprint, available online at http://penelope.mast.queensu.ca/~andrew/cgibin/pslist.cgi?papers.db, 2000.
- D.G. Luenberger, Optimization by Vector Space Methods. John Wiley and Sons (1969).
- M.B. Milam, K. Mushambi and R.M. Murray, A new computational approach to real-time trajectory generation for constrained mechanical systems, in Proc. of 39th IEEE Conference on Decision and Control 1 (2000) 845–851.
- R.M. Murray, Z. Li and S.S. Sastry, A Mathematical Introduction to Robotic Manipulation. CRC Press (1994).
- L. Noakes, G. Heinzinger and B. Paden, Cubic splines on curved spaces. IMA J. Math. Control Inform. 6 (1989) 465–473. [CrossRef] [MathSciNet]
- H.J. Pesch, Real-time computation of feedback controls for constrained optimal control problems. Part 1: Neighbouring extremals. Optim. Control Appl. Methods 10 (1989) 129–145. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
- J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, pp. 272–286; 502–535. Springer-Verlag, New York, second edition (1993).
- H. Sussmann, An introduction to the coordinate-free maximum principle, in Geometry of Feedback and Optimal Control, B. Jakubczyk and W. Respondek Eds. Marcel Dekker, New York (1997) 463–557.
Volume 12, Number 1, January 2006
|Page(s)||1 - 11|
|Published online||15 December 2005|