Abstract
The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we assume that the derivations associated with the linear vector fields of the system are inner, we obtain a simpler solution and we show some results of controllability. To finish, we work with conjugation by homomorphism of Lie groups between affine systems.
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Notes
The result is valid even for affine systems that do not satisfy the commutative condition.
As we have said, this formula is the same of [3, Theorem 4.1]. We are redoing the calculations just to give an explicit description of ϕB(t, g, u).
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de Oliveira, J., Santana, A.J. & Stelmastchuk, S.N. The General Solution for Affine Control Systems on Lie Groups. J Dyn Control Syst 28, 423–437 (2022). https://doi.org/10.1007/s10883-022-09591-4
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DOI: https://doi.org/10.1007/s10883-022-09591-4