Co-Adjoint representation and controllability
DOI:
https://doi.org/10.22199/S07160917.1992.0001.00006Keywords:
Co-adjointAbstract
Let ? an invariant control system over Lie group G The existence of a nontrivial simplectic orbit of G is analysed, so that the Hamiltonian system equivalent to ? via the co-adjoint representation, has a vector called simplectic. This allows the construction of a strictly increasing function over the positive trajectories of ?, determining sufficient conditions for the controllability of ? over G.
References
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[ 2] Jurdjevic, V. and Kupka, I.: Control Systems on Semi-simple Lie Groups and their Homogeneous Spaces. Ann. Inst. Fourier, Grenoble, 31, 4, pp 151-179, 1981.
[ 3] Jurdjevic, V . and Sussmann, H.: Control System on Lie Groups. Journal of Differential Equations, 12 , pp 313-329, 1972.
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[7] Warner, F.: Foundations of Differentiable Manifolds and Lie Group. Scott, Foresman and Company, Glenview Illinois, 1971.
[ 2] Jurdjevic, V. and Kupka, I.: Control Systems on Semi-simple Lie Groups and their Homogeneous Spaces. Ann. Inst. Fourier, Grenoble, 31, 4, pp 151-179, 1981.
[ 3] Jurdjevic, V . and Sussmann, H.: Control System on Lie Groups. Journal of Differential Equations, 12 , pp 313-329, 1972.
[ 4] Kupka, I.: Introduction to the Theory of Systems. 16 Coloquio Brasileiro de Matemática, 1987.
[ 5] San Martín, L. and Crouch, P.: Cotrollability on Principal Fibre Bundle with Compac Structure Group. System & Control Letters, 5, pp 35-40, 1984.
[ 6] Sussmann, H.: Orbits of Families of Vector Fields and Integrability of Distributions. Transactions of the American Mathematical Society, 180, June 1973.
[7] Warner, F.: Foundations of Differentiable Manifolds and Lie Group. Scott, Foresman and Company, Glenview Illinois, 1971.
Published
2018-04-02
How to Cite
[1]
V. Ayala and L. B. Vergara, “Co-Adjoint representation and controllability”, Proyecciones (Antofagasta, On line), vol. 11, no. 1, pp. 37-48, Apr. 2018.
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