TY - GEN
T1 - Combinatorics of realizations of nilpotent control systems
AU - Kawski, Matthias
PY - 1993
Y1 - 1993
N2 - This article gives a very simple algorithm which allows to immediately write down a canonical nonlinear representation of a free nilpotent Lie algebra. Specifically, it defines a set of local coordinates and gives a formula for the components of a set of system vector fields in terms of these coordinates. The components of iterated Lie brackets of the system vector fields can also be read off easily without any further differentiation. The formulae given here are very close to Sussmann's product expansion of the Chen-Fliess series and to the chronological calculus introduced by Agrachev and Gamkrelidze.
AB - This article gives a very simple algorithm which allows to immediately write down a canonical nonlinear representation of a free nilpotent Lie algebra. Specifically, it defines a set of local coordinates and gives a formula for the components of a set of system vector fields in terms of these coordinates. The components of iterated Lie brackets of the system vector fields can also be read off easily without any further differentiation. The formulae given here are very close to Sussmann's product expansion of the Chen-Fliess series and to the chronological calculus introduced by Agrachev and Gamkrelidze.
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U2 - 10.1016/b978-0-08-041901-5.50046-4
DO - 10.1016/b978-0-08-041901-5.50046-4
M3 - Conference contribution
AN - SCOPUS:0027308425
SN - 0080419011
SN - 9780080419015
T3 - IFAC Symposia Series
SP - 251
EP - 256
BT - IFAC Symposia Series
PB - Publ by Pergamon Press Inc
T2 - Proceedings of the IFAC Symposium on Nonlinear Control Systems Design 1992
Y2 - 24 June 1992 through 26 June 1992
ER -