choose to be Equation(4.7)or(4.6). Then we would choose the fitness function J similarly to how we did above. We have used such an approach to construct a Takagi-Sugeno fuzzy system that acted as a gain scheduler. One possible advantage that the ga approach could offer over, for example, a gradient method is that it may be able to better avoid local optima and hence find the global optimum On-Line Timing of Fuzzy Systems Traditionally, genetic algorithms have been used for off-line design, search, and optimization. There are ways, however, to evolve controllers(fuzzy or conventional) while the system is operating, rather man in off-line design. Progress in this direction has been made by the introduction of the"genetic model reference adaptive controller"(GMRAC) shown in Figure 4.6. As in the FMRLC, the gmrac uses a reference model to characterize the desired performance. For the GMraC there is a genetic algorithm mat maintains a population of strings each of which represents a candidate controller. This genetic algorithm uses a process model (e. g, a linear model of the process)and data from the process to evaluate the fitness of each controller in the population. It does this evaluation at each time step by simulating out into the future with each candidate controller and forming a fitness function based on the error between the predicted output for each controller and that of the reference model. Using this fitness evaluation, the genetic algorithm propagates controllers into the next generation via the standard genetic operations. The controller that is the most fit one in the population at each time step is used to control the system Vm g2=85 plation nt.Most fit v() controller Figure 4.6 Genetic model reference adaptive controller This allows the gmrac to automatically evolve a controller from generation to generation (i.e, from one time step to the next, but of course multiple generations could occur between time steps)and hence to tune a controller in response to changes in the process or due to User change of the specifications in the reference model. Overall, the gmrac provides unique features where alternative controllers can be quickly applied to the problem if they appear useful (e.g. ess (re a new operating Oand since it has some inherent capabilities to learn via evolution of its population of controllers. It is also possible to use the genetic algorithm in on-line tuning of estimators. The closest analogy to such an approach is the use of the gradient method for on-line estimator tuning. You can adapt the gmrac approach above for such a purpose 4.5 Knowledge-Based Systems In this n we will introduce two types of knowledge-based approaches to control that can be viewed as more general forms strollers than the basic(knowledge-based) fuzzy controller. First, we provide an overview of how to use an PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cnchoose to be Equation (4.7) or (4.6). Then we would choose the fitness function J similarly to how we did above. We have used such an approach to construct a Takagi-Sugeno fuzzy system that acted as a gain scheduler. One possible advantage that the GA approach could offer over, for example, a gradient method is that it may be able to better avoid local optima and hence find the global optimum. On-Line Timing of Fuzzy Systems Traditionally, genetic algorithms have been used for off-line design, search, and optimization. There are ways, however, to evolve controllers (fuzzy or conventional) while the system is operating, rather man in off-line design. Progress in this direction has been made by the introduction of the "genetic model reference adaptive controller" (GMRAC) shown in Figure 4.6. As in the FMRLC, the GMRAC uses a reference model to characterize the desired performance. For the GMRAC there is a genetic algorithm mat maintains a population of strings each of which represents a candidate controller. This genetic algorithm uses a process model (e.g., a linear model of the process) and data from the process to evaluate the fitness of each controller in the population. It does this evaluation at each time step by simulating out into the future with each candidate controller and forming a fitness function based on the error between the predicted output for each controller and that of the reference model. Using this fitness evaluation, the genetic algorithm propagates controllers into the next generation via the standard genetic operations. The controller that is the most fit one in the population at each time step is used to control the system. y t m( ) Figure 4.6 Genetic model reference adaptive controller This allows the GMRAC to automatically evolve a controller from generation to generation (i.e., from one time step to the next, but of course multiple generations could occur between time steps) and hence to tune a controller in response to changes in the process or due to User change of the specifications in the reference model. Overall, the GMRAC provides unique features where alternative controllers can be quickly applied to the problem if they appear useful (e.g., the process (re)enters a new operating condition) and since it has some inherent capabilities to learn via evolution of its population of controllers. It is also possible to use the genetic algorithm in on-line tuning of estimators. The closest analogy to such an approach is the use of the gradient method for on-line estimator tuning. You can adapt the GMRAC approach above for such a purpose. 4.5 Knowledge-Based Systems In this section we will introduce two types of knowledge-based approaches to control that can be viewed as more general forms of controllers than the basic (knowledge-based) fuzzy controller. First, we provide an overview of how to use an PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn