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 -