# zbMATH — the first resource for mathematics

Fuzzy control and conventional control: What is (and can be) the real contribution of fuzzy systems? (English) Zbl 0924.93019
The paper is a comprehensive and in-depth study about the role of fuzzy sets in control engineering. It helps to clarify the myths and misunderstandings about the use of the technology of fuzzy sets in this area.
The presentation starts from a concise analysis of classical control by looking into several fundamental classes of problems that have been solved within this framework and highlighting those that still need to be addressed. The inherent origin of the difficulties of such unresolved control problems is underlined and the role of the designer in the development process has been identified. In this context, the benefits and disadvantages of the use of fuzzy sets are studied. The issue of stability of control systems along with a discussion of the currently existing approaches is raised as well.

##### MSC:
 93C42 Fuzzy control/observation systems 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
##### Keywords:
fuzzy control; design; stability
Full Text:
##### References:
 [1] Årzén, K.-E., Expert control: intelligent tuning of PID controllers, (), 851-873 [2] Bartos, F.J., Fuzzy logic reaches adulthood, Control eng., 50-56, (1996) [3] Babuska, R.; Verbruggen, H.B., Fuzzy modeling for control, (1996), Accepted for publication in Control Engineering Practice [4] Babuska, R.; Verbruggen, H.B., Fuzzy modeling and model-based control for nonlinear systems, () · Zbl 0952.93076 [5] Babuska, R.; Verbruggen, H.B., Fuzzy set methods for local modeling and identification, () · Zbl 0952.93076 [6] Buckley, J.J., Universal fuzzy controllers, Automatica, 28, 1245-1248, (1992) · Zbl 0775.93133 [7] Buckley, J.J., Fuzzy controller: further limit theorems for linear control rules, Fuzzy sets and systems, 36, 225-233, (1990) · Zbl 0719.93059 [8] Castro, J., Fuzzy logic controllers are universal approximators, IEEE trans. systems man cybernet., 629-635, (1995) [9] Driankov, D.; Hellendoorn, H.; Reinfrank, M., Introduction to fuzzy control, (1993), Springer Berlin [10] Frank, F.M.; Köppens-Seliger, B., New developments using AI in fault diagnosis, (), 1-12 [11] Holmblad, L.P.; Østergaard, J.J., Control of a cement kiln by fuzzy logic, (), 389-399 [12] Jansen, W.J., Stability properties of fuzzy controllers, Journal A, 36, 27-37, (1995) [13] Kosko, B., Fuzzy systems as universal approximators, IEEE trans. comput., 43, 1329-1333, (1994) · Zbl 1057.68664 [14] Kuipers, B.; Åström, K.J., The compensation and validation of heterogeneous control laws, Automatica, 30, 233-249, (1994) · Zbl 0800.93707 [15] Li, M.X.; Bruijn, P.M.; Verbruggen, H.B., Tuning cascade PID controllers using fuzzy logic, Math. comput. simulation, 37, 143-151, (1994) · Zbl 0825.93389 [16] Mamdani, E.H., Applications of fuzzy algorithms for control of simple dynamic plants, (), 1585-1588 [17] Pedrycz, W., Fuzzy control and fuzzy systems, (1993), Wiley New York · Zbl 0839.93006 [18] Pedrycz, W., Relevancy of fuzzy models, Inform. sci., 52, 285-302, (1990) · Zbl 0709.94703 [19] Pedrycz, W., Fuzzy modeling: fundamentals, construction and evaluation, Fuzzy sets and systems, 41, 1-15, (1991) · Zbl 0732.93051 [20] Ray, K.S.; Maunder, D.D., Application of the circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controllers, IEEE trans. systems man cybernet., 2, 345-349, (1984) [21] Raymond, C.; Boverie, S.; Titli, A., First evaluation of fuzzy MIMO control laws, (), Orlando [22] Richalet, J., Industrial applications of model based predictive control, Automatica, 29, 1251-1274, (1993) [23] Sugeno, M.; Kang, G.T., Structure identification of fuzzy model, Fuzzy sets and systems, 28, 15-33, (1988) · Zbl 0652.93010 [24] Sugeno, M.; Tanaka, K., Successive identification of a fuzzy model and its application to prediction of a complex system, Fuzzy sets and systems, 42, 315-334, (1991) · Zbl 0741.93052 [25] Sugeno, M.; Yasukawa, T., A fuzzy-logic-based approach to qualitative modeling, IEEE trans. fuzzy systems, 1, 7-31, (1993) [26] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE trans. systems man cybernet., 15, 1, 116-132, (1985) · Zbl 0576.93021 [27] Terano, T.; Asai, K.; Sugeno, M., Applied fuzzy systems, (1994), Academic Press Boston [28] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 135-156, (1992) · Zbl 0758.93042 [29] Wang, Li-Xin, A supervisory controller for fuzzy control systems that guarantees stability, (), 1035-1039 [30] Wang, L.-X., Adaptive fuzzy systems and control, design and stability analysis, (1994), Prentice-Hall Englewood Cliffs, NJ [31] Yager, R.R.; Filev, D.P., Unified structure and parameter identification of fuzzy models, IEEE trans. systems man cybernet., 23, 1198-1205, (1993) [32] Yager, R.R.; Filev, D.P., Essentials of fuzzy modeling and control, (1994), Wiley New York [33] Yasunobu, S.; Miyamoto, S., Automatic train operation system by predictive fuzzy control, (), 1-18 [34] Ying, H.; Siler, W.; Buckley, J.J., Fuzzy control theory: a nonlinear case, Automatica, 26, 3, 513-520, (1990) · Zbl 0713.93036 [35] Yoshinari, Y.; Pedrycz, W.; Hirota, K., Construction of fuzzy models through clustering techniques, Fuzzy sets and systems, 54, 157-165, (1993) [36] Zeng, X.J.; Singh, M.G., Approximation theory of fuzzy systems —; MIMO case, IEEE trans. fuzzy systems, 2, 162-176, (1994) [37] Zeng, X.J.; Singh, M.G., Approximation theory of fuzzy systems —; MIMO case, IEEE trans. fuzzy systems, 3, 219-235, (1995) [38] Zhao, Z.-Y.; Tomizuka, M.; Isaka, S., Fuzzy gain scheduling of PID controllers, IEEE trans. systems man cybernet., 23, 5, 1392-1398, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.