Modeling and control of an unstable system using probabilistic fuzzy inference system

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Abstract

A new type Fuzzy Inference System is proposed, a Probabilistic Fuzzy Inference system which model and minimizes the effects of statistical uncertainties. The blend of two different concepts, degree of truth and probability of truth in a unique framework leads to this new concept. This combination is carried out both in Fuzzy sets and Fuzzy rules, which gives rise to Probabilistic Fuzzy Sets and Probabilistic Fuzzy Rules. Introducing these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed and this involves fuzzification, inference and output processing. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. In this paper a Probabilistic Fuzzy Inference System is applied for modeling and control of a highly nonlinear, unstable system and also proved its effectiveness.

[1] H.A. MEGHDADI, R. MOHAMMED and T. AKBARZADEH: Probabilistic fuzzy logic and probabilistic fuzzy system. IEEE Int. Fuzzy System Conf., (2001), 1127-1130.

[2] J. BART KOSKO: Fuzziness vs probability. Int. J. General Systems, 17 (1990), 211-240.

[3] H. BUSTINCE and P. BURILLO: Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning. Fuzzy Sets Systems, 113 (2000), 205-219.

[4] CHAIO-SHIUNG CHEN and WEN-LIANG CHEN: Robust adaptive sliding-mode control using fuzzy modeling for an inverted pendulum system. IEEE Trans. on Industrial Electronics, 45 (1998), 297-306.

[5] A.COLUBI, C.FERNANDEZ-GARCIA and M.A. GIL: Simulation of random fuzzy variables: an empirical approach to statistical/probabilistic studies with fuzzy experimental data. IEEE Trans. on Fuzzy Systems, 10 (2003), 384-390.

[6] M.B. GORZALCZANY: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Systems, 21 (1987), 1-17.

[7] S. GUILLAUME: Designing fuzzy inference systems from data: An interpretability-oriented review. IEEE Trans. on Fuzzy Systems, 9 (2001), 426-443.

[8] J.M. MENDEL and R.I.B JOHN: Type-2 fuzzy sets made simple. IEEE Trans. on Fuzzy Systems, 10 (2002), 117-127.

[9] P. LIANG and F. SONG: What does a probabilistic interpretation of fuzzy sets mean? IEEE Trans. on Fuzzy Systems, 2 (1996), 200-205.

[10] M. LAVIOLETTE and J.W. SEAMAN JR: Unity and diversity of fuzziness-from a probability viewpoint. IEEE Trans. on Fuzzy Systems, 2 (1994), 38-42.

[11] C.C. LEE: Fuzzy logic in control systems. Fuzzy logic controller. Part I, Part II. IEEE Trans. on Systems, Man, and Cybernetics, 20 (1990), 404-435.

[12] N.N. KARNIK, J.M. MENDEL and Q. LIANG: Type-2 fuzzy logic systems. IEEE Trans. on Fuzzy Systems, 7 (1999), 643-658.

[13] N.N. KARNIK and J.M. MENDEL: Introduction to type-2 fuzzy logic systems. IEEE World Congress on Computational Intelligence, 2 (1998), 915-920.

[14] E. SIVARAMAN and S. ARULSELVI: Modeling of an inverted pendulum based on fuzzy clustering techniques. Elsevier - Expert Systems with Applications, 38 (2011), 13942-13949.

[15] M. SUGENO and T. YASUKAWA: A fuzzy-logic-based approach to qualitative modeling. IEEE Trans. on Fuzzy Systems, 1 (1993), 7-31.

[16] T. TAKAGI and M. SUGENO: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on Systems, Man, and Cybernetics, 15 (1985), 116-132.

[17] C.W. TAO, S.J. TAUR, T.W. HSIEH and C.L. TSAI: Design of a fuzzy controller with fuzzy swing-up and parallel distributed pole assignment schemes for an inverted pendulum and cart system. IEEE Trans. on Control Systems Technology, 16 (2008), 1277-1288.

[18] WEN-SHYONG YU and CHIH-JEN SUN: Fuzzy model based adaptive control for a class of nonlinear systems. IEEE Trans. on Fuzzy Systems, 9 (2001), 413-425.

[19] WEN-HSIEN HO, JINN-TSONG TSAI and JYH-HORNG CHOU: Robust quadratic-optimal control of TS-fuzzy-model-based dynamic systems with both elemental parametric uncertainties and norm-bounded approximation error. IEEE Trans. on Fuzzy Systems, 17 (2009), 518-530.

[20] X.L. WANG and J.M. MENDEL: Generating fuzzy rules by learning from examples. IEEE Trans. on Systems, Mann, and Cybernetics, 22 (1992), 1414-1427.

[21] XIAN-XIA ZHANG, HAN-XIONG LI and SHAO-YUAN LI: Analytical study and stability design of a 3-D fuzzy logic controller for spatially distributed dynamic systems. IEEE Trans. on Fuzzy Systems, 16 (2008), 1613-1625.

[22] R.R. YAGER: Fuzzy modeling for intelligent decision making under uncertainty. IEEE Trans. on Systems, Man, and Cybernetics, part B: Cybernetics, 30 (2000), 60-70.

[23] ZHI LIU and HAN-XIONG LI: A probabilistic fuzzy logic system for modeling and control. IEEE Trans. on Fuzzy Systems, 13 (2005), 848-856.

[24] L.A. ZADEH: Discussion: probability theory and fuzzy logic are complementary rather than competitive. Technometrics, 37 (1995), 271-276.

[25] L.A. ZADEH: The concept of a linguistic variable and its application to approximate reasoning - I. Information Sciences, 8 (1975), 199-249.

Archives of Control Sciences

The Journal of Polish Academy of Sciences

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IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.565

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