Controllability of nonlinear discrete systems

Jerzy Klamka

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 173-180
  • ISSN: 1641-876X

Abstract

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Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.

How to cite

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Klamka, Jerzy. "Controllability of nonlinear discrete systems." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 173-180. <http://eudml.org/doc/207577>.

@article{Klamka2002,
abstract = {Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.},
author = {Klamka, Jerzy},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {discrete systems; controllability; 2-D systems; nonlinear covering operators; nonlinear systems; 2-D discrete-time systems; local controllability; constrained controls},
language = {eng},
number = {2},
pages = {173-180},
title = {Controllability of nonlinear discrete systems},
url = {http://eudml.org/doc/207577},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Klamka, Jerzy
TI - Controllability of nonlinear discrete systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 173
EP - 180
AB - Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.
LA - eng
KW - discrete systems; controllability; 2-D systems; nonlinear covering operators; nonlinear systems; 2-D discrete-time systems; local controllability; constrained controls
UR - http://eudml.org/doc/207577
ER -

References

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  1. Graves L.M. (1950): Some mapping theorems. - Duke Math.J., Vol. 17, No.1, pp. 111-114. Zbl0037.20401
  2. Kaczorek T. (1985): Two-Dimensional Linear Systems. - Berlin: Springer. Zbl0593.93031
  3. Kaczorek T. (1993): Linear Control Systems. - New York: Wiley. Zbl0784.93003
  4. Kaczorek T. (1995): U-reachability and U-controllability of 2-D Roesser model. - Bull. Polish Acad. Sci. Tech. Sci., Vol. 43, No. 1, pp. 31-37. Zbl0849.93010
  5. Klamka J. (1988a): M-dimensional nonstationary linear discrete systems in Banach spaces. - Proc. 12-th IMACS World Congress, Paris, Vol. 4, pp. 31-33. 
  6. Klamka J. (1988b): Constrained controllability of 2-D linear systems. - Proc. 12-th IMACS World Congress, Paris, Vol. 2, pp. 166-169. 
  7. Klamka J. (1991a): Complete controllability of singular 2-D system. - Proc. 13-th IMACS World Congress, Dublin, pp. 1839-1840. 
  8. Klamka J. (1991b): Controllability of Dynamical Systems. -Dordrecht: Kluwer. Zbl0732.93008
  9. Klamka J. (1992): Controllability of nonlinear 2-D systems. - Bull.Polish Acad. Sci. Tech. Sci., Vol. 40, No. 2, pp. 125-133. Zbl0767.93004
  10. Klamka J. (1993): Controllability of dynamical systems-A survey. - Arch.Contr. Sci., Vol. 2, No. 3, pp. 281-307. Zbl0818.93002
  11. Klamka J. (1994): Constrained controllability of discrete 2-D linear systems. - Proc. IMACS Int. Symp. Signal Processing, Robotics and Neural Networks, Lille, France, pp. 166-169. 
  12. Klamka J. (1995): Constrained controllability of nonlinear systems. - IMA J. Math. Contr. Inf., Vol. 12, No. 2, pp. 245-252. Zbl0840.93014
  13. Klamka J. (1996): Controllability of 2-D nonlinear systems. - Proc.2-nd World Congress Nonlinear Analysis, Athens, Greece, pp. 196-199. 
  14. Robinson S.M. (1986): Stability theory for systems of inequalities. Part II: Differentiable nonlinear systems. - SIAM J. Numer. Anal., Vol. 13, No. 4, pp. 1261-1275. 

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