Due to the above relationships between fuzzy systems and neural networks, some would like to view fuzzy systems and neural networks as identical areas This is. however not the case for the following reasons a There are classes of neural networks(e.g, dynamic neural networks )that may have a fuzzy system analog, but if so it would have to include not only standard fuzzy components but some form of a differential equation There are certain fuzzy systems that have no clear neural analog. Consider, for example, certain"fuzzy dynamic systems"[48, 167. We can, however, envision how you could go about"designing a neural analog to such fuzzy systems a The neural network has traditionally been a"black box"approach where the weights and biases are trained (e.g using gradient methods like back-propagation)using data, often without using extra heuristic knowledge we often have In fuzzy systems you can incorporate heuristic information and use data to train them. This last difference is often quoted as being one of the advantages of fuzzy systems over neural networks, at least for some applications Regardless of the differences, it is important to note that many methods in neural control (i.e, when we use a neural network for the control of a system) are quite similar to those in adaptive fuzzy control. For instance, since the fuzzy system and radial basis function neural network can be linearly parameterized, we can use them as the identifier structures in direct or indirect adaptive control schemes and use gradient or least squares methods to update the parameters. Indeed, we could have used neural networks as the structure that we trained for all of the identification methods. In this sense we can use neural networks in system identification, estimation, and prediction, and as a direct ( fixed) controller that is trained with input-output data. Basically, to be fluent with the methods of adaptive fuzz systems and control, you must know the methods of neural controland vice versa 4.4 Genetic Algorithms A genetic algorithm(GA)uses the principles of evolution, natural selection, and genetics from natural biological systems in a computer algorithm to simulate evolution. Essentially, the genetic algorithm is an optimization technique that performs a parallel, stochastic, but directed search to evolve the most fit population. In this section we will introduce the genetic algorithm and explain how it can be used for design and tuning of fuzzy systems 4.4.1 Genetic Algorithms: A Tutorial The genetic algorithm borrows ideas from and attempts to simulate Darwin's theory on natural selection and Mendel's work in genetics on inheritance. The genetic algorithm is ah optimization technique that evaluates more than one area of the search space and can discover more than one solution to a problem. In particular, it provides a stochastic optimization method where if it"gets stuck"at a local optimum, it tries to simultaneously find other parts of the search space and jump out"of the local optimum to a global one Representation and the Population of Individuals The "fitness function ures the fitness of an individual to survive in a population of individuals. The genetic algorithm will seek to maximize the fitness function Je)by selecting the individuals that we represent with 6. To represent the genetic algorithm in a computer, we make 6 a string. In particular, we show such a string in Figure 4. 4.A tring is a chromosome in a biological system. It is a string of "genes"that can take on different"alleles. In a computer PDF文件使用" pdffactory Pro"试用版本创建ww, fineprint,com,cnDue to the above relationships between fuzzy systems and neural networks, some would like to view fuzzy systems and neural networks as identical areas. This is, however, not the case for the following reasons: ¡ There are classes of neural networks (e.g., dynamic neural networks) that may have a fuzzy system analog, but if so it would have to include not only standard fuzzy components but some form of a differential equation component. ¡ There are certain fuzzy systems that have no clear neural analog. Consider, for example, certain "fuzzy dynamic systems" [48, 167]. We can, however, envision how you could go about "designing a neural analog to such fuzzy systems. ¡ The neural network has traditionally been a "black box" approach where the weights and biases are trained (e.g., using gradient methods like back-propagation) using data, often without using extra heuristic knowledge we often have. In fuzzy systems you can incorporate heuristic information and use data to train them. This last difference is often quoted as being one of the advantages of fuzzy systems over neural networks, at least for some applications. Regardless of the differences, it is important to note that many methods in neural control (i.e., when we use a neural network for the control of a system) are quite similar to those in adaptive fuzzy control. For instance, since the fuzzy system and radial basis function neural network can be linearly parameterized, we can use them as the identifier structures in direct or indirect adaptive control schemes and use gradient or least squares methods to update the parameters. Indeed, we could have used neural networks as the structure that we trained for all of the identification methods. In this sense we can use neural networks in system identification, estimation, and prediction, and as a direct (fixed) controller that is trained with input-output data. Basically, to be fluent with the methods of adaptive fuzzy systems and control, you must know the methods of neural control—and vice versa. 4.4 Genetic Algorithms A genetic algorithm (GA) uses the principles of evolution, natural selection, and genetics from natural biological systems in a computer algorithm to simulate evolution. Essentially, the genetic algorithm is an optimization technique that performs a parallel, stochastic, but directed search to evolve the most fit population. In this section we will introduce the genetic algorithm and explain how it can be used for design and tuning of fuzzy systems. 4.4.1 Genetic Algorithms: A Tutorial The genetic algorithm borrows ideas from and attempts to simulate Darwin's theory on natural selection and Mendel's work in genetics on inheritance. The genetic algorithm is ah optimization technique that evaluates more than one area of the search space and can discover more than one solution to a problem. In particular, it provides a stochastic optimization method where if it "gets stuck" at a local optimum, it tries to simultaneously find other parts of the search space and "jump out" of the local optimum to a global one. Representation and the Population of Individuals The "fitness function" measures the fitness of an individual to survive in a population of individuals. The genetic algorithm will seek to maximize the fitness function J(θ) by selecting the individuals that we represent with θ . To represent the genetic algorithm in a computer, we make θ a string. In particular, we show such a string in Figure 4.4. A string is a chromosome in a biological system. It is a string of "genes" that can take on different "alleles." In a computer PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn