About the solutions of linear control systems on Lie groups

Authors

  • Víctor Ayala Universidad de Tarapaca.
  • Adriano Da Silva Universidade Estadual de Campinas.
  • Eyüp Kizil Universidade de São Paulo.

DOI:

https://doi.org/10.4067/S0716-09172016000400010

Keywords:

Linear control systems, Lie groups, solutions, sistemas de control lineal, grupos de Lie, soluciones

Abstract

In this paper we prove in details the completeness of the solutions of a linear control system on a connected Lie group. On the other hand, we summarize some results showing how to compute the solutions. Some examples are given.

Author Biographies

Víctor Ayala, Universidad de Tarapaca.

Instituto de Alta Investigación.

Adriano Da Silva, Universidade Estadual de Campinas.

Instituto de Matemática.

Eyüp Kizil, Universidade de São Paulo.

Instituto de ciências matemáticas e de computação.

References

[1] Ayala, V. and Tirao, J. Linear control systems on Lie groups and controllability, Eds. G. Ferreyra et al., Amer. Math. Soc., Providence, RI, (1999).

[2] Ayala, V. and San Martin, L., Controllability properties of a class of control systems on Lie groups. Lectures Notes in Control and Information Science, (2001).

[3] Ayala, V. and Da Silva, A., Controllability of linear systems on Lie groups with finite semisimple center. Submitted to SIAM Journal, (2016).

[4] Ayala, V, and Silva, A., Control sets of linear systems on Lie groups. Submitted to Nonlinear Differential Equations and Applications, (2016).

[5] Ayala, V, Kizil, E. and Tribuzy, I., On an algoritm for finding derivations of Lie algebras. Proyecciones Mathematical Journal, Vol 31, No.1, pp. 81-90, (2012.)

[6] Da Silva, A., Controllability of linear systems on solvable Lie groups, SIAM Journal on Control and Optimization, Vol 54, No. 1, pp. 372-390, (2016).

[7] Jouan, Ph., Controllability of linear Systems on Lie group, Journal of Dynamics and Control Systems, Vol 17, pp. 591-616, (2011).

[8] Jouan, Ph. and Dath M., Controllability of linear systems on low dimensional nilpotent and solvable Lie groups, Journal of Dynamics and Control Systems, Vol 22, pp. 207-225, (2016).

[9] Jouan, Ph., Equivalence of control systems with linear systems on Lie groups and homogeneous spaces, ESAIM: Control Optimization and Calculus of Variations, Vol 16, pp. 956-973, (2010).

Published

2017-03-23

How to Cite

[1]
V. Ayala, A. Da Silva, and E. Kizil, “About the solutions of linear control systems on Lie groups”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 491-503, Mar. 2017.

Issue

Section

Artículos