C. Karr and E. J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--53, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a variety of problems. Fuzzy logic controllers tuned by genetic algorithms. Some fundamentals of theory and description of individual components, as well as the early implementations of fuzzy logic controllers tuned by genetic algorithms can be found in a series of publications [57] 68] 69] [70], 71] 72] 61] 22] 73] 74] and [75] Fuzzy logic controllers learning by genetic algorithms. In [76] two different approaches to apply genetic algorithms to fuzzy logic controllers are described. The first approach uses the knowledge base as the individual of the genetic system, while ....

Karr C. L., Fuzzy control of pH using genetic algorithms, IEEE Trans. Fuzzy Syst. FS, 146-153, 1993

....based on a neural network trained by temporal back propagation. Lee et.al. 10] proposed a self organizing fuzzified basis function based on the competitive learning scheme. A more recent technique in implementing adaptive or self tuning FLCs is by using genetic algorithms (GAs) Karr and Gentry [11,12] applied GA in the tuning of fuzzy membership functions which was applied to a pH control process and a cart pole balancing system. Kim et.al. 13] used a similar method, however, with different shapes of fuzzy membership functions applied to different processes. Varsek et.al. 14] used GAs to tune ....

Karr,C.L. and Gentry,E.J. Fuzzy Control of pH Using Genetic Algorithms, IEEE Trans.on Fuzzy Systems, Vol.1, No.1. pp46-53, Feb.1993

....have similar performance) and deceptive, since a little modi cation may cause huge e ects on the performance of each system. The use of genetic algorithms to automatically adjust (part of) the parameters of a fuzzy system has attracted attention of researches from di erent engineering areas [3] [4], 5] 6] 7] 8] As shown in Herrera and Verdegay [9] genetic algorithms can be considered as ecient techniques for selecting high performance parameters to design a fuzzy system. However, some factors must be carefully analyzed in the process of fuzzy system design. The most important ....

C. L. Karr and E. J. Gentry,\Fuzzy control of ph using genetic algorithms," IEEE Transactions on Fuzzy Systems,vol. 1, no. 1, pp. 46-53, 1993.

....fuzzy sliding mode controllers, very useful in control of manipulators. In a different approach several authors have implemented the self organization as a neural network training problem, in a neuro fuzzy architecture ( 4] 7] 11] 15] or as a genetic algorithm optimization problem ( 1] [6]) Usually those approaches require knowledge about the process to initialize the procedure and, because of neural networks training algorithms, they are computationally hard ; moreover, they are complex to implement in real time control of dynamic systems where two identical situations are very ....

C. A. Karr and E. J. Gentry, Fuzzy Control of PH using genetic algorithms, IEEE Trans. on Fuzzy Systems 1 (1993) 46-53.

....But we can extract classes of problems which can be described by a common function. For example the class of problems where a parameter x(t) shall adopt a special value c, we can use the time weighted error f = maxtime X t=start t(x(t) Gamma c) 2 as it is stated in several articles [10, 6]. The problem is to select appropriate initial conditions to test a controller s performance. Some authors suggest to select a condition out of the entire parameter space randomly [13, 10] This includes very extreme conditions for a controller that is not able to manage even easy problems. So we ....

....ones. This is, because the optimized rule base seems to be very good, and because the cart pole problem is a relative artificial and easy problem. IV. Other Approaches In this section we shortly review other approaches and discuss the differences to ours. The Approach of C. Karr C. Karr [6, 5] uses genetic algorithms to alter just the shape of the fuzzy sets used in a given rule base. Each parameter of a fuzzy set (left , middle , and right point) is coded as a seven bit binary number. The parameters of all sets are concatenated to a bit string used for the genetic algorithm. The ....

C. Karr, Fuzzy Control of pH using Genetic Algorithms. IEEE Transactions on Fuzzy Systems 1 (1993), 46--53.

.... [36, 27, 28] Computers Operations Research, 76] Engineering Applications of Artificial Intelligence, 35, 59] European Journal of Operational Research, 77] IEEE Computer Society Technical Committee on Microprogramming and Microarchitecture, 82] IEEE Transactions on Fuzzy Systems, [54] Journal of Chemical Information and Computer Sciences, 26] Sci. Comput. Autom. USA) 55] Soc. Pet. Eng. AIME Pap. SPE, 58] SuperMenu, 124] Systems Science (Poland) 89] Trends in Analytical Chemistry, 23] total 21 articles in 17 journals 4.3 Theses The following two lists contain ....

....Bounsaythip, Catherine, 29, 30] Branke, Jurgen, 112, 113, 114, 115, 116, 117] Buydens, Lutgarde M. C. 22, 12, 23, 24, 25, 26, 27, 28] Cockcroft, Victor, 11] Dai, Ping, 72] East, Ian R. 102, 103, 104, 105, 106] Fang, J. H. 58] Freeman, L. M. 41, 42, 47, 49] Gentry, Edward J. [51, 54, 57] Goldberg, David E. 37, 39] Goos, Janne, 90] Haataja, Juha, 124] Hakkarainen, Juha, 96, 97] Harper, T. R. 50, 59, 60] Hatcher, W. J. 50, 59, 60] Hekanaho, Jukka, 108, 11, 109, 110] Heuvel, H. M. 22, 28] Hohfeld, Markus, 119] Hohn, Christian, 63, 64, 65, 66, 67] Huber, ....

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Charles L. Karr and Edward J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--52, 1993. ga:Karr93b.

....Control Theory Appl. 538, 610] IEEE Aerospace and Electronic Systems Magazine, 81] IEEE Control Systems, 80] IEEE Expert, 178, 192] IEEE Spectrum, 95] IEEE Transaction on Power Systems, 666] IEEE Transactions on Evolutionary Computing, 640] IEEE Transactions on Fuzzy Systems, [78, 706, 113, 132, 542, 709, 712, 223, 629, 444] IEEE Transactions on Industrial Electronics, 193, 204, 307] IEEE Transactions on Networking, 585] IEEE Transactions on Plasma Science, 316] IEEE Transactions on Power Delivery, 656] IEEE Transactions on Power Systems, 576] IEEE Transactions on Signal Processing, 317] IEEE Transactions ....

....Furuta, H. 384, 390] Gac ogne, L. 16, 74, 337] Gan, Meng, 114] Gao, Xinbo, 396] G.Attolico, 306] Gen, M. 545, 710, 146, 716, 720, 302] Gen, Mitsuo, 465, 486, 729, 708, 104, 529, 547, 552, 422, 718] Genshe, Chen, 704] Genther, H. 738] Gentry, E. J. 156] Gentry, Edward J. [730, 443, 689, 444, 348] George, R. 34, 380, 449] George, Roy, 169] George, Suju M. 17] Geyer Schulz, Andreas, 406] Ghazi, R. 504] Gil, Joonmin, 267] Giordana, A. 439] Girshgorn, S. L. 285, 669] Giuclea, M. 261] Glass, C. 323] Glesner, Manfred, 75, 738, 182] Glorennec, Pierre Yves, 18, ....

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Charles L. Karr and Edward J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46-52, 1993. ga:Karr93b.

.... IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications, 177] IEEE Transactions on Circuits and Systems for Video Technology, 631] IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, 695, 972] IEEE Transactions on Fuzzy Systems, [553] IEEE Transactions on Magnetics, 670] IEEE Transactions on Microwave Theory and Techniques, 717] IEEE Transactions on Power Delivery, 356] IEEE Transactions on Power Systems, 191, 849] IEEE Transactions on Systems, Man, and Cybernetics, 230, 262, 280, 471, 1041] IEICE Transactions on ....

....Michael L. 575, 576] Garigliano, Roberto, 751, 752] Garis, Hugo de, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 214] Gaspart, P. 265] Gawelczyk, Andreas, 771] Geigel, Joe, 982] Gen, Mitsuo, 368] Genshe, Chen, 1077] Gentry, Edward J. [553, 556] George, Felicity A. W. 848] George, R. 810] Germay, Noel, 369, 370] Gibson, G. M. 359] Gibson, G. 358] Giles, P. A. 774, 775] Gillis, P. 1042] Giordana, A. 371, 372] Glass, C. 134] Glen, Robert C. 373, 374] Gold, Sonke Sonnich, 921] Goldammer, E. von, 963] ....

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Charles L. Karr and Edward J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--52, 1993. ga:Karr93b.

....inverted pendulum problem [53, 56] collisionfree movement of a robot in a simulated corridor environment [70] robust motion control of a mobile robot [82] etc. Another study of the use of genetic algorithms in the design and implementation of fuzzy logic controllers has been considered in [54], where a GA is proposed to generate membership functions for a pH control process that is present in a number of mineral and chemical industries. Genetic algorithms have also been used to optimize the Sugeno fuzzy model [93, 98] that was described previously. For this purpose the chromosome ....

C.L. Karr and E.J. Gentry. Fuzzy Control of pH Using Genetic Algorithms. IEEE Trans. on Fuzzy Systems, 1(1):46--53, 1993.

....by GAs. For brevity s sake we will limit this section to a few contributions. These methods differ mostly in the order or the selection of the various FC components that are tuned (termsets, rules, scaling factors) One of the precursors in this quest was C. Karr (Karr, 1991b, Karr, 1991a, Karr, 1993) who used GAs to modify the membership functions in the termsets of the variables used by the FCs. Karr used a binary encoding to represent three parameters defining a membership value in each termset. The binary chromosome was the concatenation of all termsets. The fitness function was a ....

C.L. Karr. Fuzzy control of ph using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1:46--53, 1993.

....searching the poorly understood, irregular and complex membership function space with improved performance. Successful application of this approach has been demonstrated in spacecraft rendezvous [5] cart pole balancing [6] linear motion of cart [7] three term control [8] and pH value control [9]. However, the design scope of these FLC membership functions is limited by internally linear triangular trapezoidal shapes and by binary encoding. This paper develops genetic algorithms for designing fuzzy logic controllers using sophisticated membership functions that intrinsically reflect the ....

C.L. Karr and E.J. Gentry, "Fuzzy control of pH using genetic algorithms," IEEE Trans. Fuzzy Systems, vol.1, no.1, pp.46-53, Jan. 1993.

....functions. Piecewise linear functions. The most broadly used parameterized membership functions in the field of GFSs are triangles, in some cases these are isosceles ( 7, 13, 31, 42] and other times they are irregular ( 33] A second possibility are trapezoidal membership functions ( 32] Each parameter of the function consti NS NM ZR PS PM PB X Y NB NM NS ZR PS PM PB R1: If X is NB then Y is NB NB R2: If X is NM then Y is NM R3: If X is NS then Y is NS R4: If X is ZR then Y is ZR a) Descriptive Knowledge Base Xl Xr Yl Yr R5: If X is PS then Y is PS R6: If X is PM then Y ....

.... PM R7: If X is PB then Y is PB R1: If X is R2: If X is R3: If X is R4: If X is then Y is then Y is then Y is then Y is b) Approximate Knowledge Base Figure 7: Descriptive versus Approximate fuzzy models tutes a gene of the chromosome that may be a binary code representing the parameter ( 7, 31, 32, 33] or a real number (the parameter itself, 13, 24, 42] Differentiable functions. Gaussian, bell and sigmoidal are examples of parameterized differentiable functions. These membership functions have been broadly applied in different fuzzy neural systems ( 37] but radial functions ( 47] ....

C.L. Karr, E.J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems 1 (1993) 46-53.

.... use gradient free optimization schemes, such as genetic algorithms [22] 19] simulated annealing [44] 45] downhill Simplex method [68] and random method [63] 88] In particular, use of genetic algorithms for neural network controllers can be found in [113] for fuzzy logic controllers, see [39], 52] 38] If the plant model is not available, we can apply reinforcement learning [2] to find a working controller directly. The close relationship between reinforcement learning and dynamic programming was addressed in [3] 110] Other variants of reinforcement learning includes temporal ....

C. L. Karr and E. J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Trans. on Fuzzy Systems, 1(1):46--53, February 1993.

....Learning for Fuzzy rules) an EL system that faces efficiently some of these problems. We also show some applications of ELF to conceptually interesting problems. EVOLUTIONARY LEARNING AGORITHMS AND FUZZY SYSTEMS Since 1989 [15] GAs have been adopted to identify sub optimal FLCs [20] 18][16][19] There have been also proposals to extend the LCS approach to Fuzzy Classifier Systems [21] 22] 23] Learning could be applied to at least 3 different aspects of an FLC: concept definition, state relevance, and the relationship between state and action. Concept definition People tend to ....

....These labels are the terms on which the FLC operates, and the membership functions ground each label on data, since they provide a mean to translate numbers into interpretations. The problem of learning membership functions with EL Algorithms has been addressed by many people (e.g. 20] 18][16]. In some of these approaches the set of rules is defined a priori and the GA is used to optimize the shape of the membership functions [14] In this case the GA tunes the FLC. The same can be said for those systems where fuzzy rules have a specific set of membership functions each [18] 21] In ....

C. L. Karr, E. J. Gentry, Fuzzy control of pH using genetic algorithms. IEEE Trans. on Fuzzy Systems., Vol.1, no.1, pp. 46-53, 1993.

.... into two main groups: the piecewise linear functions (trapezoidal and triangular, Figure 2) and the differentiable functions (Gaussian, bell and sigmoidal, Figure 3) Triangular functions are used in [4, 9, 22] symmetric, Figure 2 center) and [13] Figure 2 right) trapezoidal functions in [10] and differentiable functions in [25] radial functions) and [14] Gaussian functions) Each coefficient constitutes a gene of the chromosome that may be a binary code (representing the coefficient) 4, 9, 10, 13, 25] or a real number (the coefficient itself) 14, 22] b c d a b a c b a 1 0 Fig. ....

.... in [4, 9, 22] symmetric, Figure 2 center) and [13] Figure 2 right) trapezoidal functions in [10] and differentiable functions in [25] radial functions) and [14] Gaussian functions) Each coefficient constitutes a gene of the chromosome that may be a binary code (representing the coefficient) [4, 9, 10, 13, 25] or a real number (the coefficient itself) 14, 22] b c d a b a c b a 1 0 Fig. 2. Examples of parameterized piece wise linear functions. 0 1 a a a b b 1 2 1 e 1 2 1 1 0 0 Fig. 3. Examples of parameterized differentiable functions. Evolving sets of rules. The set of rules describing a certain ....

[Article contains additional citation context not shown here]

C.L. Karr and E.J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--53, February 1993.

....by GAs. For brevity s sake we will limit this section to a few contributions. These methods differ mostly in the order or the selection of the various FC components that are tuned (termsets, rules, scaling factors) C. Karr, one of the precursors in this quest [see Karr (1991b) Karr (1991a) Karr (1993)] used GAs to modify the membership functions in the termsets of the variables used by the FCs. Karr used a binary encoding to represent three parameters defining a membership value in each termset. The binary chromosome was the concatenation of all termsets. The fitness function was a quadratic ....

Karr, C.L. (1993). Fuzzy control of ph using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1:46--53.

....having a great influence over the whole FLC performance. Some efforts have been made to improve system performance by incorporating learning mechanisms to modify rules and or MF. The application of Genetic Algorithms (GAs) to FLCs in such a way has recently produced some interesting works [1, 3, 4, 6, 10, 11]. GAs are probabilistic search and optimization procedures based on natural genetics, working with finite strings of bits that represent the set of parameters of the problem, and with a fitness function to evaluate each one of these strings. This paper proposes two methods to apply GAs to FLCs ....

Karr C.L. and Gentry E.J., "Fuzzy Control of pH Using Genetic Algorithms". IEEE Transactions on Fuzzy Systems, vol 1, num 1, pp 46-53. Feb. 1993.

.... parameterized functions may be classified into two main groups: the piece wise linear functions (trapezoidal and triangular) and the differentiable functions (Gaussian, bell and sigmoidal) Triangular functions are used in [7, 8, 9] symmetric) and [10] non symmetric) trapezoidal functions in [11] and differentiable functions in [12] radial functions) and [13] Gaussian functions) Each coefficient constitutes a gene of the chromosome that may be a binary code (representing the coefficient) 7, 8, 11, 10, 12] or a real number (the coefficient itself) 9, 13] The rule base of a fuzzy ....

.... functions are used in [7, 8, 9] symmetric) and [10] non symmetric) trapezoidal functions in [11] and differentiable functions in [12] radial functions) and [13] Gaussian functions) Each coefficient constitutes a gene of the chromosome that may be a binary code (representing the coefficient) [7, 8, 11, 10, 12] or a real number (the coefficient itself) 9, 13] The rule base of a fuzzy logic controller may be coded by means of a fuzzy relation, a fuzzy decision table or a set of fuzzy rules. The use of sets of fuzzy rules have demonstrated the advantage of reducing the dimension of the knowledge base ....

C.L. Karr and E.J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--53, February 1993.

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C. Karr and E. J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46--53, 1993.

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C. L. Karr and E. J. Gentry, "Fuzzy control of pH using genetic algorithms," IEEE Transactions of Fuzzy Systems, Vol. 1, 1993, pp. 46-53.

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Charles L. Karr and Edward J. Gentry. Fuzzy control of pH using genetic algorithms. IEEE Transactions on Fuzzy Systems, 1(1):46 -- 53, 1993.

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Karr,C.L. and Gentry,E.J., 1993, Fuzzy Control of pH Using Genetic Algorithms, IEEE Trans.on Fuzzy Systems, Vol.1, No.1., p46-53.

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Karr, C.A. and E.J. Gentry(1993). Fuzzy Control of PH using genetic algorithms. IEEE Trans. on Fuzzy Systems, vol. 1, n 1, pp 46-53.

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C. L. Karr, E. J. Gentry, 1993 "Fuzzy Control of pH Using Genetic Algorithms", IEEE Transactions on Fuzzy Systems, Vol.1, No.1, pp.46-53.

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C. L. Karr, E. J. Gentry, "Fuzzy Control of pH Using Genetic Algorithms," IEEE Transactions on Fuzzy Systems, Vol.1, No.1, pp.46-53, 1993.

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