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- 1
- A. AGRACHEV AND R. GAMKRELIDZE, Chronological
algebras and nonstationary vector fields,
Journal Soviet Math., 17 (1979), pp. 1650-1675.
- 2
- C. ALTAFINI, Explicit Wei-Norman formulae for
matrix Lie groups, submitted to Systems Control Lett.,
Elsevier Science, Feb. 2002, available at
http://www.sissa.it/~altafini
. - 3
- J. G. F. BELINFANTE AND B. KOLMAN, A Survey of
Lie Groups and Lie Algebras with Applications and Computational
Methods. Society for Industrial and Applied Mathematics, 1972.
- 4
- N. BOURBAKI, Lie Groups and Lie Algebras, Part
I: Chapters 1-3, Hermann, Great Britain, 1975.
- 5
- R. W. BROCKETT AND J. M. C. CLARK, The geometry
for the conditional density functions, in Analysis and Optimization of
Stochastic Systems, O. Jacobs et al., eds., Academic Press, New York,
1980, pp. 299-310.
- 6
- B. CHAMPAGNE, W. HEREMAN AND P. WINTERNITZ,
The computer calculation of Lie point symmetries of large systems
of differential equations,
Comput. Phys. Comm., 66 (1991), pp. 319-340.
- 7
- M. COHEN DE LARA, Finite-dimensional filters.
Part I: The Wei-Norman technique, SIAM J. Control Optim., 35 (1997), pp. 980-1001.
- 8
- V.T. COPPOLA AND N.H. MCCLAMROCH, Spacecraft
attitude control, in Control System Applications, W. S. Levine, ed.,
CRC Press, 2000.
- 9
- M. DAHLEH, A. PEIRCE, H.A. RABITZ AND V. RAMAKRISHNA,
Control of molecular motion, Proc. of the IEEE, 84 (1996), pp. 7-15.
- 10
- M. H. A. DAVIS AND S. I. MARCUS, An introduction
to nonlinear filtering, in Stochastic Systems: The Mathematics of
Filtering and Identification and Applications, M. Hazewinkel and
J. Willems, eds., D. Reidel, Dordrecht, Netherlands, 1981, pp. 55-75.
- 11
- P. FEINSILVER AND R. SCHOTT, Algebraic Structures and Operator Calculus, Vol. III. Mathematics and Its Applications, Kluwer Academic Publishers, 1996.
- 12
- M. FLIESS, Réalisation locale des
systèmes non linéaires, algèbres de Lie filtrées
transitives et séries génératrices non commutatives,
Inventiones Mathematicae, 71 (1983), pp. 521-537.
- 13
- R. GILMORE, Lie Groups, Lie Algebras, and Some
of Their Applications, John Wiley & Sons, Inc., 1974.
- 14
- M. HALL, The Theory of Groups, Macmillan,
1959.
- 15
- H. HERMES, Nilpotent and high-order
approximations of vector field systems, SIAM Rev., 33 (1991),
pp. 238-264.
- 16
- A. ISIDORI, Nonlinear Control Systems -- An
Introduction. ed., Springer-Verlag Berlin, 1989.
- 17
- M. KAWSKI AND H. J.SUSSMANN, Noncommutative
power series and formal Lie-algebraic techniques in nonlinear control
theory, in Operators, Systems, and Linear Algebra, U. Helmke,
D. Prätzel-Wolters and E. Zerz, eds., Teubner, (1997), pp.111-128.
- 18
- M. KAWSKI, The combinatorics of nonlinear
controllability and noncommuting flows, Abdus Salam ICTP Lecture
Notes series, 8 (2002), pp. 223-312.
- 19
- P. S. Krishnaprasad, S. I. Marcus, M. Hazewinkel. Current
algebras and the identification problem. Stochastics, v. 11, 1983,
pp. 65-101.
- 20
- G. LAFFERRIERE AND H. J. SUSSMANN, A
differential geometric approach to motion planning, in Nonholonomic
Motion Planning, Z. Li, and J. F. Canny, eds., Kluwer
Academic Publishers, 1993, pp. 235-270.
- 21
- M.A.A. van Leeuwen. LiE, A software package for Lie group
computations. Euromath Bulletin 1, n. 2, 1994.
- 22
- W. MAGNUS, On the exponential solution of
differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954),
pp. 649-673.
- 23
- S. MARCUS, Algebraic and geometric methods in
nonlinear filtering, SIAM J. Control Optim., 22 (1984), pp. 817-844.
- 24
- G. MELANSCON AND C. REUTENAUER, Lyndon words,
free algebras and shuffles, Canadian J. Math., XLI (1989), pp. 577-591.
- 25
- G. MELANSCON AND C. REUTENAUER, Combinatorics
of Hall trees and Hall words, J. Comb. Th., Ser. A 59 (1992),
pp. 285-299.
- 26
- H. MICHALSKA AND M. TORRES-TORRITI,
A geometric approach to feedback stabilization of nonlinear systems
with drift, Systems Control Lett.,
50 (2003), pp. 303-318.
- 27
- R.M. MURRAY, Z. LI AND S.S. SASTRY, A Mathematical
Introduction to Robotic Manipulation, CRC Press, 1994.
- 28
- D. OCONE, Finite dimensional estimation algebras
and nonlinear filtering, in Stochastic Systems: The Mathematics of
Filtering and Identification and Applications, M. Hazewinkel and J.C.
Willems, eds., Reidel, Dordrecht, 1981.
- 29
- R. PALAIS, Global Formulation of the Lie Theory of
Transformation Groups, v. 22, Mem. Amer. Math. Soc., AMS, 1957.
- 30
- C. REUTENAUER, Free Lie algebras,
Clarendon Press,
1993.
- 31
- E. ROCHA, On computation of the logarithm of
the Chen-Fliess series for nonlinear systems, Lecture Notes in Control
and Information Sciences - Vol. 281: Nonlinear and Adaptive Control:
NCN4 2001, Springer-Verlag Heidelberg, (2003), pp. 317-326.
- 32
- S.S. SASTRY, Nonlinear Systems: Analysis,
Stability and Control, Springer-Verlag New York, Inc.,
1999.
- 33
- D. H. SATTINGER AND O. L. WEAVER, Lie Groups and
Algebras with Applications to Physics, Geometry and Mechanics,
Springer-Verlag New York, Inc., 1986.
- 34
- M.-P. SCH¨UTZENBERGER, Sur une propriété
combinatoire des algèbres de Lie libres pouvant être utilisée
dans un problème de mathématiques appliquées, Séminaire
P. Dubreil, Faculté des Sciences, Paris, 1958.
- 35
- J. M. SELIG, Geometrical Methods in Robotics,
Springer-Verlag New York, Inc., 1996.
- 36
- J.-P. SERRE, Lie Algebras and Lie groups,
W. A. Benjamin, New York, 1965.
- 37
- A. I. SHIRSHOV, Bases of free Lie algebras,
Algebra i Logika Sém., 1 (1962), pp. 14-19.
- 38
- W.-H. STEEB, Continuous Symmetries, Lie
Algebras, Differential Equations and Computer Algebra, World
Scientific Co., 1996.
- 39
- R.S. STRICHARTZ, The Campbell-Baker-Hausdorff-Dynkin
formula and solutions of differential equations, J. Funct. Anal., 72 (1987), pp. 320-345.
- 40
- H. J. SUSSMANN, Lie brackets and local
controllability: a sufficient condition for scalar-input systems,
SIAM J. Control Optim., 21 (1983), pp. 686-713.
- 41
- H. J. SUSSMANN, A product expansion for the
Chen series, in Theory and Applications of Nonlinear Control Systems,
C. Byrnes and A. Lindquist, eds., Elsevier Science Publishers B. V.
(North Holland), (1986), pp.323-335.
- 42
- H. J. SUSSMANN, A general theorem on local
controllability, SIAM J. Control Optim., 25 (1987), pp. 158-194.
- 43
- V. S. VARADARAJAN, Lie Groups, Lie Algebras, and
their Representations, Springer-Verlag New York, Inc., 1984.
- 44
- X. G. VIENNOT, Algébres de Lie Libres et
Monoïdes Libres, Lecture Notes in Mathematics, Vol. 691, Springer,
Berlin, 1978.
- 45
- J. WEI AND E. NORMAN, On global representations
of the solutions of linear differential equations as products of
exponentials, Proc. Amer. Math. Soc., 15 (1964), pp. 327-334.
- 46
- Computer Algebra Systems - A Practical
Guide. M. J. Wester Editor, John Wiley & Sons Ltd.,
1999.
Books on Maple Programming
- 47
- A. HECK, Introduction to Maple, Second Edition.
Springer-Verlag New York, Inc., 1996.
- 48
- B. W. CHAR, ET AL., Maple V Library
Reference Manual. Springer-Verlag, 1991
- 49
- B. W. CHAR, ET AL., Maple V Language
Reference Manual. Springer-Verlag, 1991
- 50
- R. A. NICOLAIDES AND N. WALKINGTON, Maple a
Comprehensive Introduction. Cambridge University Press, 1996.
Resources on Internet
- 51
- Computer Languages:
http://dmoz.org/Computers/Programming/Languages/
- 52
- Functional Programming FAQ:
http://www.cs.nott.ac.uk/~gmh/faq.html
- 53
- GiNaC (GNU is Not a CAS):
http://www.ginac.de/
- 54
- Reduce CAS:
http://www.uni-koeln.de/REDUCE/
- 55
- Computer Algebra Information Network (Europe):
http://www.mupad.de/CAIN/
- 56
- Symbolic Mathematical Computation Information
Center (US):
http://www.SymbolicNet.org/
Miguel Attilio Torres-Torriti
2004-05-31