Abstract
This paper introduces a new tool for intelligent control and identification. A robust and reliable learning and reasoning mechanism is addressed based upon fuzzy set theory and fuzzy associative memories. The mechanism storesa priori an initial knowledge base via approximate learning and utilizes this information for identification and control via fuzzy inferencing. This architecture parallels a well-known scheme in which memory implicative rules are stored disjunctively. We call this process afuzzy hypercube. Fuzzy hypercubes can be applied to a class of complex and highly nonlinear systems which suffer from vagueness uncertainty and incomplete information such as fuzziness and ignorance. Evidential aspects of a fuzzy hypercube are treated to assess the degree of certainty or reliability. The implementation issue using fuzzy hypercubes is raised, and finally, a fuzzy hypercube is applied to fuzzy linguistic control.
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References
Zadeh, L.A., Fuzzy sets,Inform. Contr. 8, 338–353 (1965).
Kosko, B., Fuzzy associative memories, inFuzzy Expert Systems, (ed. A. Kandel), Addison-Wesley, New York (1987).
Mamdani, E.H., Østergaard, J.J. and Lembessis, E., Use of fuzzy logic for implementing rule-based control of industrial processes,Advances in Fuzzy Sets, Possibility Theory, and Applications, Plenum Press, pp. 307–323 (1983).
Kaufmann, A. and Gupta, M.M., (eds.),Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York (1985).
Dempster, A., Upper and lower probabilities induced by a multivaried mapping,Ann. Math. Stat. 38, 325–339 (1967).
Shafer, G.,A Mathematical Theory of Evidence, Princeton University Press, New Jersey (1976).
Fu, K.S., Learning control systems and intelligent control systems: an intersection of artificial intelligence and automatic control,IEEE Trans. Automat. Control AC-16, 70–72 (1971).
Saridis, G.N., Intelligent robotic control,IEEE Trans. Automat. Control AC-28, 547–557 (1983).
Albus, J.S., A new approach to manipulator control: the cerebellar model articulation controller (cmac),Trans. ASME, J. Dynam. Systems Meas. Control 00, 220–227 (1975).
Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes,IEEE Trans. Systems Man Cybernet SMC-3, 28–44 (1973).
Tong, R.M., Some properties of fuzzy feedback systems,IEEE Trans. Systems Man Cybernet SMC-10(6), 327–330 (1980).
Togai, M. and Chiu, S., A fuzzy accelerator and a programming environment for real-time fuzzy control, inProc. 2nd IFSA Congress, (Tokyo, Japan), pp. 147–151 (1987).
Klir, G.J. and Folger, T.A.,Fuzzy Sets, University, and Information, Prentice Hall, New Jersey (1988).
Kang, H. and Vachtsevanos, G., Nonlinear fuzzy control based on the vector fields of the phase portrait assignment algorithm, inProc. 28th American Control Conf., (San Diego, CA), pp. 1479–1484 (1990).
Meystel, A., Intelligent control: issues and perspectives,Proc. IEEE Workshop Intelligent Control, pp. 1–15 (1985).
Lee, C.C., Fuzzy logic control systems: fuzzy logic controller — parts i, ii,IEEE Trans. Systems Man Cybernet SMC-20, 404–435 (1990).
Kandel, A.,Fuzzy Mathematical Techniques with Applications, Addison-Wesley, Mass. (1986).
Zadeh, L.A., Fuzzy logic and its application to approximate reasoning,Information Processing,74, 591–594 (1973).
Dubois, D. and Prade, H., On several representations of an uncertain body of evidence, inFuzzy Information and Decision Processes, (eds. M.M. Gupta and E. Sanchez), North-Holland, Amsterdam pp. 167–181 (1982).
Yager, R.R., Level sets for membership evaluation of fuzzy subsets, inFuzzy Set and Possibility Theory: Recent Developments, (ed. R.R. Yager), Pergamon Press, Oxford pp. 90–97 (1982).
Vachtsevanos, G., Kang, H., Kim, I. and Cheng, J., Managing uncertainty and ignorance for system fault detection and identification, inProc. 5th Int. Symp. on Intelligent Control (Philadelphia, PA), pp. 558–563 (1990).
Togai, M. and Watanabe, H., Expert system on a chip: an engine for real-time approximate reasoning,IEEE Expert Systems Magazine 1, 55–62 (1986).
Kang, H. and Vachtsevanos, G.J., Model reference fuzzy control, inProc. 28th IEEE Conf. Dec. and Contr. (Tampa, FL), pp. 751–756 (1989).
Braae, M. and Rutherford, D.A., Selection of parameters for a fuzzy logic controller,Fuzzy Sets and Systems 2, 185–199 (1979).
Kang, H. and Vachtsevanos, G.J., An intelligent strategy to robot coordination and control, inProc. 29th IEEE Conf. Dec. and Contr. (Honolulu, Hawaii), pp. 2208–2213, (1990).
Kang, H., Intelligent/adpative control stategies for robot manipulators. PhD thesis, Georgia Institute of Technology, Atlanta (1989).
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Kang, H., Vachtsevanos, G. Fuzzy hypercubes: Linguistic learning/reasoning systems for intelligent control and identification. J Intell Robot Syst 7, 215–232 (1993). https://doi.org/10.1007/BF01257820
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DOI: https://doi.org/10.1007/BF01257820