Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach

Changjiu Zhou

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 3, page 411-421
  • ISSN: 1641-876X

Abstract

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A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the 'words' represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.

How to cite

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Zhou, Changjiu. "Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach." International Journal of Applied Mathematics and Computer Science 12.3 (2002): 411-421. <http://eudml.org/doc/207598>.

@article{Zhou2002,
abstract = {A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the 'words' represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.},
author = {Zhou, Changjiu},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fuzzy control; computing with words; pole balancing mobile robot; standard fuzzy arithmetic; Lyapunov synthesis; constrained fuzzy arithmetic; perception-based information; stability; fuzzy arithmetic},
language = {eng},
number = {3},
pages = {411-421},
title = {Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach},
url = {http://eudml.org/doc/207598},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Zhou, Changjiu
TI - Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 3
SP - 411
EP - 421
AB - A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the 'words' represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.
LA - eng
KW - fuzzy control; computing with words; pole balancing mobile robot; standard fuzzy arithmetic; Lyapunov synthesis; constrained fuzzy arithmetic; perception-based information; stability; fuzzy arithmetic
UR - http://eudml.org/doc/207598
ER -

References

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