A Fuzzy Control Heuristic Applied to Non-linear Dynamic System Using a Fuzzy Knowledge Representation

Authors

  • Felisa M. Cordova University of Santiago of Chile Ecuador 3769. Estacion Central Chile, Santiago E-mail:
  • Guillermo Leyton University of La Serena Benavente 980

Keywords:

Fuzzy Systems, Knowledge Representation, Heuristics, Nonlinear Dynamic Systems

Abstract

This paper presents the design of a fuzzy control heuristic that can be applied for modeling nonlinear dynamic systems using a fuzzy knowledge representation. Nonlinear dynamic systems have been modeled traditionally on the basis of connections between the subsystems that compose it. Nevertheless, this model design does not consider some of the following problems: existing dynamics between the subsystems; order and priority of the connection between subsystems; degrees of influence or causality between subsystems; particular state of each subsystem and state of the system on the basis of the combination of the diverse states of the subsystems; positive or negative influences between subsystems. In this context, the main objective of this proposal is to manage the whole system state by managing the state combination of the subsystems involved. In the proposed design the diverse states of subsystems at different levels are represented by a knowledge base matrix of fuzzy intervals (KBMFI). This type of structure is a fuzzy hypercube that provides facilities operations like: insert, delete, and switching. It also allows Boolean operations between different KBMFI and inferences. Each subsystem in a specific level and its connectors are characterized by factors with fuzzy attributes represented by membership functions. Existing measures the degree of influence among the different levels are obtained (negatives, positives). In addition, the system state is determined based on the combination of the statements of the subsystems (stable, oscillatory, attractor, chaos). It allows introducing the dynamic effects in the calculation of each output level. The control and search of knowledge patterns are made by means of a fuzzy control heuristic. Finally, an application to the co-ordination of the activities among different levels of the operation of an underground mine is developed and discussed.

References

D. Alahakoon, S. K. Halgamuge, and B. Srinivasan, Dynamic self organizing maps with controlled growth for knowledge discovery, IEEE Trans. Neural Networks, Vol.11:601-614, 2000. http://dx.doi.org/10.1109/72.846732

F. Cordova, L. Canete, L. Quezada, F. Yanine, An Intelligent Supervising System for the Operation of an Undergound Mine, International Journal of Computers, Communications and Control, Vol. III: 259-269, 2008.

M. Gupta, R.K. Ragade,Yager, Advances in Fuzzy Sets Theory and applications, North Holland, Amsterdam, 1979.

B. Kosko, Fuzzy Ingineering. Prentice Hall, 1997.

G. Martinez, Servente and Pasquini,Sistemas Inteligentes, NL Nueva Libreria, Argentina, 2003.

T. McNeill, Fuzzy Logic a Practical Approach. Academic Press, 1997.

H. Roman, Sobre Entropias Fuzzy, Tesis de doctorado, Universidad de Campinas, Brasil, 1989.

E. Schnaider, A. Kandel, Applications of the Negation Operator in Fuzzy Production Rules, Fuzzy Sets and Systems, Vol. 34: 293-299, Noth Holland, 1990.

W. Silder, J. Buckley, Fuzzy expert system and fuzzy reasoning, John Wiley and Sons Inc., New Jersey, 416, 2005.

U. Tsoukalas, Fuzzy and Neural Approaches in Engineering. Wiley Interscience, 1997.

S. Welstead, Neural Network and Fuzzy Logic Applications in C++. Wiley Interscience, 1994.

L.A. Zadeh, The role of fuzzy logic in the management of uncertainly in Expert Systems, Aproximate Reasoning in Expert Systems, Elservier Science Pub., North Holland, 3-31, 1985.

L.A. Zadeh et al (eds.), From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence, Editing House of Romanian Academy, 2008.

Zadeh, L.A., Outline of a new approach to the analysis of a complex systems and decision processed, IEEE Trans. Syst. Man Cybern., Vol. 3: 28-44, 1973. http://dx.doi.org/10.1109/TSMC.1973.5408575

L.A. Zadeh, Fuzzy sets and fuzzy information: granulation theory, Beijing Normal University Press, Beijing, 1997.

L.Zhong, W.A. Halang,G. Chen, Integration of Fuzzy Logic and Chaos Theory, Springer- Verlag, Berlin Heidelberg, 2006.

Published

2010-12-01

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