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1、 中国石油大学(北京)本科毕业设计 第 20 页 文献翻译原文Evolution of Fuzzy Controllers and ApplicationsD.K. Pratihar and N.B. Hui: Evolution of Fuzzy Controllers and Applications, Studies inComputational Intelligence (SCI) 66, 4769 (2007)SummaryThe present chapter deals with the issues related to the evolution of optimal fu
2、zzy logic controllers (FLC) by proper tuning of its knowledge base (KB), using different tools, such as least-square techniques, genetic algorithms, backpropagation (steepest descent) algorithm, ant-colony optimization, reinforcement learning, Tabu search, Taguchi method and simulated annealing. The
3、 selection of a particular tool for the evolution of the FLC, generally depends on the application. Some of the applications have also been included in this chapter.Keywords: Fuzzy logic controller, Evolution, Least-square technique,Genetic-fuzzy system, Neural-fuzzy system, Ant-colony optimization,
4、 Reinforcement learning, Tabu search, Taguchi method, Simulated annealing1 IntroductionReal-world problems are generally associated with different types of uncertainties. In the past, considerable effort has been made to model these uncertainties. Prior to 1965, it was considered that probability th
5、eory working based on Aristotelian two-valued logic was the sole agent available to deal with uncertainties. This particular logic uses the concept of the classical crisp set. That is a set with a fixed boundary. Prof. Zadeh developed the conceptof fuzzy sets, in the year 1965 1. Those are the sets
6、having the vague boundaries.He argued that probability theory can handle only one out of several different types of possible uncertainties. Thus, there are uncertainties, which cannot be dealt with by using the probability theory. Taking an example,in which Mr. X requests Mr. Y, to bring some red ap
7、ples for him from the market. There are two uncertainties at least, which relate to the following:(i) the availability of the apples, and (ii) a guarantee that the apple is red.Depending on the season, there is a probability of obtaining the apples, which varies between 0 and 1. But, the colour red
8、cannot be defined by the classical set. It is not between red (1) and not-red (0). In the fuzzy set, the colour red can be defined as follows (Fig. 3.1) using the concept of membership of an element to a class. That is the function value (): If the colour is perfectly red PR, then it may be said red
9、 with a membership value of 1.0; if it is R,then it is considered to be red with a membership value of 0.65; if it is slightly red SR, then it is red with a membership value of 0.39. If it is not red (NR),then also it is red with a membership value of 0.0. In this way, the uncertainty related to the
10、 colour of the apples can be handled. Thus, a fuzzy set may be considered to be a more general concept than the classical set.The concept of fuzzy set theory has been used in a number of applications,such as the Fuzzy Logic Controller (FLC), fuzzy clustering, fuzzy mathematical programming, fuzzy gr
11、aph theory and other examples. Out of all such applications, FLC is the most popular application for the following reasons (i) ease of understanding and implementations, (ii) ability to handle uncertainty etc. An exact mathematical formulation of the problem is not required for the development of an
12、 FLC. This feature makes it a natural choice for solving complex real-world problems. These are either difficult to model mathematically or the mathematical model becomes highly non-linear. It is to be noted that a fuzzy logic controller was first developed by Mamdani and Assilian, in the year 1975
13、2. The concept of fuzzy set was published in theFig. 3.1. A schematic diagram explaining the concept of membership function distribution.year 1965. Human beings have the natural ability of determining the inputoutput relationships of a process. The behavior of a human being is modeled artificially,
14、when designing a suitable FLC. The performance of an FLC depends on its knowledge base (KB), which in turn consists of both Data Base (DB) and a Rule Base (RB). The DB consists of data related to membership function distributions of the variables of the process to be controlled. Designing a proper K
15、B of an FLC is a difficult task, which may be implemented in one of the following ways: Optimization of the data base only, Optimization of the rule base only, Optimization of the data base and rule base in stages, Optimization of the data base and rule base simultaneously.The membership function di
16、stributions are assumed to be either Linear such as, triangular, trapezoidal or Non-Linear. The Non-Linear can be Gaussian, bell-shaped, sigmoidal in nature. To design and develop a suitable FLC for controlling a process, its variables need to be expressed in the form of some linguistic terms (such as VN: Very Near, VF: Very Far, A: Ahead for example). The relationships between the input (antecedent) and
