# Symmetries of control systems

Banach Center Publications (1996)

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

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topSamokhin, 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

top- [1] P. H. M. Kersten, The general symmetry algebra structure of the underdetermined equation ${u}_{x}={\left({v}_{x}x\right)}^{2}$, J. Math. Phys. 32 (1991), 2043-2050. Zbl0738.34007
- [2] I. M. Anderson, N. Kamran and P. Olver, Interior, exterior and generalized symmetries, preprint, 1990.
- [3] A. P. Krishenko, personal communication.
- [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] G. N. Yakovenko, Solving a control system using symmetries, in: Applied Mechanics and Control Processes, MFTI, Moscow, 1991, 17-31 (in Russian).
- [6] G. N. Yakovenko, Symmetries by state in control systems, MFTI, Moscow, 1992, 155-176 (in Russian).
- [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] 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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