×

Towards a paradigm for fuzzy logic control. (English) Zbl 0845.93048

Although fuzzy logic controllers (FLC) are suitable for a wide range of control applications and show good performance, there are still problems which are expected to be solved. Till now, little has been done to study mathematically the stability of FLC and to provide repeatable algorithms for designing FLC. Also while designing FLC, there are so many parameters that it is difficult to make a choice for them. The present paper is intended to lay a foundation for fuzzy logic control design, constructing a class of FLC that is suitable for a broad range of applications. Some scalar definitions relevant to FLC are extended to the multidimensional case, including such concepts as vector numbers and membership vectors. A rigorous mathematical definition for the function \(g(x)\) synthesized by a fuzzy associative memory is given. It is shown that for the existence and uniqueness of solutions in a closed-loop system with a fuzzy logic controller, the fuzzy associative memory function \(g(x)\) must be Lipschitz. An algorithm for designing a FLC is proposed in the paper. Also the scalar and the two-dimensional cases are studied in detail.

MSC:

93C42 Fuzzy control/observation systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93C35 Multivariable systems, multidimensional control systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bracewell, R., (The Fourier Transform and Its Applications (1965), McGraw-Hill: McGraw-Hill New York) · Zbl 0149.08301
[2] Buckley, J. J., Universal fuzzy controllers, Automatica, 28, 1245-1248 (1992) · Zbl 0775.93133
[3] Chen, G.; Ying, H., On the stability of fuzzy PI control systems, (Proc. Internat. and Conf. on Industrial Fuzzy Control and Intelligent Systems (1993))
[4] Chiu, S.; Chand, S., Fuzzy controller design and stability analysis for an aircraft model, (Proc. Fuzzy Control Workshop for Industrial Applications (1991), Texas A&M University), 89-95
[5] Commuri, S., Neural net and fuzzy logic control, (PhD dissertation (1995), Department of Electrical Engineering, The University of Texas at Arlington), (in progress) 1995
[6] Gupta, M. M.; Qi, J., Theory of T-norms and fuzzy inference methods, Fuzzy Sets and Syst., 40, 431-450 (1991) · Zbl 0726.03017
[7] Jamshidai, M.; Vadiee, N.; Ross, T. J., (Fuzzy Logic and Control (1993), Prentice Hall: Prentice Hall Englewood Cliffs, NJ)
[8] (Kandel, A.; Langholz, G., Fuzzy Control Systems (1994), CRC Press: CRC Press Boca Raton, FL) · Zbl 0941.00502
[9] Kawaji, S.; Matsunaga, N., Fuzzy control of VSS type and its robustness, (Kandel, A.; Langholz, G., Fuzzy Control Systems (1994), CRC Press: CRC Press Boca Raton, FL), 226-242 · Zbl 0844.93049
[10] Kosko, B., (Neural Networks and Fuzzy Systems (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ)
[11] Kreinovich, V.; Quintana, C.; Lea, R., What procedure to choose while designing a fuzzy control?, (Proc. Fuzzy Control Workshop for Industrial Applications (1991), Texas A&M University), 123-130
[12] Langari, R.; Tomizuka, M., Analysis of stability of a class of fuzzy linguistic controllers with internal dynamics, (Proc. ASME Winter Annual Meeting. Proc. ASME Winter Annual Meeting, Paper 91-WA-DSC-13 (1991))
[13] Lee, C. C., Fuzzy logic control systems: fuzzy logic controller—Part I, IEEE Trans. Syst., Man, Cyber., SMC-20, 404-415 (1990) · Zbl 0707.93036
[14] Liu, K.; Lewis, F. L., Robust control techniques for general dynamic systems, J. Intel. Robotic Syst., 6, 33-49 (1992) · Zbl 0778.93018
[15] Mizumoto, M., Fuzzy controls under various reasoning methods, Inf. Sci., 45, 129-151 (1988)
[16] Precup, R.-E.; Preitl, S., On a fuzzy digital PID predictor controller, (Proc. IEEE Mediterranean Symp. on New Directions in Control Theory and Automation (1994))
[17] Slotine, J.-J. E.; Li, W., (Applied Nonlinear Control (1991), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ)
[18] Smith, S. M.; Nokleby, B. R.; Comer, D. J., A computational approach to fuzzy logic controller design and analysis using cell state space methods, (Kandel, A.; Langholz, G., Fuzzy Control Systems (1994), CRC Press: CRC Press Boca Raton, FL), 397-427 · Zbl 0853.93068
[19] Wang, L.-X., (Adaptive Fuzzy Systems and Control (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ)
[20] Ying, H., A nonlinear fuzzy controller with linear control rules is the sum of a global two-dimensional multilevel relay and a local nonlinear proportional-integral controller, Automatica, 29, 499-505 (1993) · Zbl 0772.93050
[21] Ying, H., General analytical structure of typical fuzzy controllers and their limiting structure theorems, Automatica, 29, 1139-1143 (1993) · Zbl 0782.93062
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.