Symmetries of control systems

Alexey Samokhin

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 337-342
  • ISSN: 0137-6934

Abstract

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Symmetries of the control systems of the form u t = f ( t , u , v ) , u ∈ ℝ n , v ∈ ℝ m are studied. Some general results concerning point symmetries are obtained. Examples are provided.

How to cite

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Samokhin, Alexey. "Symmetries of control systems." Banach Center Publications 33.1 (1996): 337-342. <http://eudml.org/doc/262814>.

@article{Samokhin1996,
abstract = {Symmetries of the control systems of the form $u_t = f(t,u,v)$, $u ∈ ℝ^n$, $v ∈ ℝ^m$ are studied. Some general results concerning point symmetries are obtained. Examples are provided.},
author = {Samokhin, Alexey},
journal = {Banach Center Publications},
keywords = {point and higher symmetries; control system; Lie algebra; point symmetries},
language = {eng},
number = {1},
pages = {337-342},
title = {Symmetries of control systems},
url = {http://eudml.org/doc/262814},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Samokhin, Alexey
TI - Symmetries of control systems
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 337
EP - 342
AB - Symmetries of the control systems of the form $u_t = f(t,u,v)$, $u ∈ ℝ^n$, $v ∈ ℝ^m$ are studied. Some general results concerning point symmetries are obtained. Examples are provided.
LA - eng
KW - point and higher symmetries; control system; Lie algebra; point symmetries
UR - http://eudml.org/doc/262814
ER -

References

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  1. [1] P. H. M. Kersten, The general symmetry algebra structure of the underdetermined equation u x = ( v x x ) 2 , J. Math. Phys. 32 (1991), 2043-2050. Zbl0738.34007
  2. [2] I. M. Anderson, N. Kamran and P. Olver, Interior, exterior and generalized symmetries, preprint, 1990. 
  3. [3] A. P. Krishenko, personal communication. 
  4. [4] Y. N. Pavlovskiĭ and G. N. Yakovenko, Groups admitted by dynamical systems, in: Optimization Methods and their Applications, Nauka, Novosibirsk, 1982, 155-189 (in Russian). 
  5. [5] G. N. Yakovenko, Solving a control system using symmetries, in: Applied Mechanics and Control Processes, MFTI, Moscow, 1991, 17-31 (in Russian). 
  6. [6] G. N. Yakovenko, Symmetries by state in control systems, MFTI, Moscow, 1992, 155-176 (in Russian). 
  7. [7] J. W. Grizzle and S. I. Marcua, The structure of nonlinear control systems possessing symmetries, IEEE Trans. Automat. Control 30 (1985), 248-257. 
  8. [8] A. J. van der Schaft, Symmetries and conservation laws for Hamiltonian systems with inputs and outputs: A generalization of Noether's theorem, Systems Control Lett. 1 (1981), 108-115. Zbl0482.93038

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