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Title: Motion on lie groups and its applications in control theory
Authors: Cariñena, José F. 
Clemente-Gallardo, Jesús 
Ramos, Arturo 
Keywords: Drift-free control systems; Wei-Norman method; motion in Lie groups and homogeneous spaces; reduction
Issue Date: 2003
Citation: Reports on Mathematical Physics. 51:2-3 (2003) 159-170
Abstract: The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the method proposed by Wei and Norman for linear systems, and a reduction procedure. This last method allows us to reduce the equation on a Lie group G to that on a subgroup H, provided a particular solution of an associated problem in G/H is known. These methods are shown to be very appropriate to deal with control systems on Lie groups and homogeneous spaces, through the specific examples of the planar rigid body with two oscillators and the front-wheel driven kinematic car.
Rights: openAccess
Appears in Collections:FCTUC Eng.Electrotécnica - Artigos em Revistas Internacionais

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