Null controllability on Lie groups
DOI:
https://doi.org/10.4067/S0716-09172013000100005Keywords:
Derivations of Lie algebras, Linear control system, Null controllability.Abstract
We prove an extension of a classical result for null controllability of linear control systems on Euclidean spaces, to linear control systems on a connected Lie group G, assumed to be simply connected and nilpotent.References
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[2] V. Ayala, Controllability of nilpotent systems. Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications, Warszawa, Poland, pp. 3546, (1995).
[3] V. Ayala, W. Kliemann and F. Vera, Isochronous sets of invariant control systems. Systems and Control Letters 60, pp. 937-942, (2011).
[4] V. Ayala, J. Rodriguez, I. Tribuzy and C. Wagner, Solutions of singular control systems on Lie groups, to appear in Journal of Dynamics and Control Systems, (2012).
[5] V. Ayala and L. San Martin, Controllability Properties of a Class of Control Systems on Lie Groups. Lectures Notes in Control and Information Science, Vol 1, N 258, pp. 83-92, (2001).
[6] V. Ayala, E. Kizil and I. Tribuzy, On an algoritm for finding derivations of Lie algebras. Proyecciones Journal of Mathematics, Vol 31, N 1, pp. 81-90, (2012).
[7] V. Jurdjevic and H. J. Sussmann, Control Systems on Lie Groups. Journal of Differential Equations 12, pp. 313-329, (1972).
[8] V. Jurdjevic and I. Kupka, Control Systems on Semi-simple Lie Groups and their Homogeneous Spaces. Ann. Inst. Fourier, Grenoble 31, pp. 151-179, (1981).
[9] P. Jouan, Controllability of Linear Control Systems on Lie Groups, Journal of Dynamical and Control Systems 17, pp. 591-616, (2011).
[10] A.O. Nielsen, Unitary representations and coadjoint orbits of low dimensional nilpotent Lie groups, Queen’s Papers in Pure and Applied Mathematics, 63, (1983).
[11] Y. Sachkov, Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces. Progress in Science and Technology, Series on Contemporary Mathematics and Applications, Thematical Surveys, Vol. 59, (1998).
[12] Y. Sachkov, Controllability of affine right-invariant systems on solvable Lie groups. Discrete Mathematics and Theoretical Computer Science 1, pp. 239-246, (1997).
[13] L. San Martin and P. Crouch, Controllability on Principal Fibre Bundle with Compact Structre Group. System and Control Letters 5, pp. 35- 40, (1984).
[14] V.S. Varadaradjan, Lie groups, Lie algebras and their representations. Prentice-Hall (1974).
[2] V. Ayala, Controllability of nilpotent systems. Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications, Warszawa, Poland, pp. 3546, (1995).
[3] V. Ayala, W. Kliemann and F. Vera, Isochronous sets of invariant control systems. Systems and Control Letters 60, pp. 937-942, (2011).
[4] V. Ayala, J. Rodriguez, I. Tribuzy and C. Wagner, Solutions of singular control systems on Lie groups, to appear in Journal of Dynamics and Control Systems, (2012).
[5] V. Ayala and L. San Martin, Controllability Properties of a Class of Control Systems on Lie Groups. Lectures Notes in Control and Information Science, Vol 1, N 258, pp. 83-92, (2001).
[6] V. Ayala, E. Kizil and I. Tribuzy, On an algoritm for finding derivations of Lie algebras. Proyecciones Journal of Mathematics, Vol 31, N 1, pp. 81-90, (2012).
[7] V. Jurdjevic and H. J. Sussmann, Control Systems on Lie Groups. Journal of Differential Equations 12, pp. 313-329, (1972).
[8] V. Jurdjevic and I. Kupka, Control Systems on Semi-simple Lie Groups and their Homogeneous Spaces. Ann. Inst. Fourier, Grenoble 31, pp. 151-179, (1981).
[9] P. Jouan, Controllability of Linear Control Systems on Lie Groups, Journal of Dynamical and Control Systems 17, pp. 591-616, (2011).
[10] A.O. Nielsen, Unitary representations and coadjoint orbits of low dimensional nilpotent Lie groups, Queen’s Papers in Pure and Applied Mathematics, 63, (1983).
[11] Y. Sachkov, Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces. Progress in Science and Technology, Series on Contemporary Mathematics and Applications, Thematical Surveys, Vol. 59, (1998).
[12] Y. Sachkov, Controllability of affine right-invariant systems on solvable Lie groups. Discrete Mathematics and Theoretical Computer Science 1, pp. 239-246, (1997).
[13] L. San Martin and P. Crouch, Controllability on Principal Fibre Bundle with Compact Structre Group. System and Control Letters 5, pp. 35- 40, (1984).
[14] V.S. Varadaradjan, Lie groups, Lie algebras and their representations. Prentice-Hall (1974).
Published
2013-06-23
How to Cite
[1]
V. Ayala and E. Kizil, “Null controllability on Lie groups”, Proyecciones (Antofagasta, On line), vol. 32, no. 1, pp. 61-72, Jun. 2013.
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