Title :
Explicit Wei-Norman formulae for matrix Lie groups
Author :
Altafini, Claudio
Author_Institution :
SISSA-ISAS, Int. Sch. for Adv. Studies, Trieste, Italy
Abstract :
The Wei-Norman formula locally relates the Magnus solution of a system of linear time-varying ODE with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed, based only on the structure constants of the Lie algebra generated by the ODEs.
Keywords :
Lie algebras; matrix algebra; nonlinear differential equations; time-varying systems; Lie algebra; Magnus solution; closed form expression; explicit Wei-Norman formulae; linear time-varying ODE; matrix Lie groups; nonlinear differential equations; structure constants; Algebra; Books; Control systems; Differential equations; Jacobian matrices; Motion planning; Nonlinear equations; Robot kinematics; Solid modeling; Time varying systems;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184251
