第5章 Perspectives on Fuzzy Control 教学内容 本章讲述模糊控制与传统控制的相互关系、模糊神经网络控制、模糊控制和遗传算法的相互联系与区别、 模糊控制与基于知识系统的交叉和融合。 教学重点 重点内容是讲述模糊控制与传统控制的相互关系,模糊系统与神经网络、遗传算法、基于知识的学习系 统的相互联系以及交叉融合。 教学难点 对模糊控制与传统控制、神经网络控制、遗传算法以及基于知识的系统的区别和联系的准确把握和理 解,学会用发展和联系的观点看待智能控制学科的发展。 教学要求 要求学生基本了解模糊控制与传统控制、神经网络控制、遗传算法以及基于知识的系统的区别和联系. 通过本章的学习,进一步加深对智能控制特点的理解,学会用发展和联系的观点看待智能控制学科的发展 从而培养学生创常新意识和能力,形成正确的工作方法。 5.1 Overview Fuzzy control does not exist as an isolated topic devoid of relationships to other fields, and it is important to understand how it relates to these other fields in order to strengthen your understanding of it. We have emphasized that fuzzy control has its foundations in conventional control and that there are many relationships to techniques, ideas, and methodologies there. Fuzzy control is also an"intelligent control"technique, and hence there are certain relationships between it and other intelligent control methods. In this chapter we will provide a brief overview of some of the basic relationships between fuzzy control and other control methods. This will give the reader who has a good understanding of fuzzy control a glimpse of related topics in other areas. Moreover, it will give the reader who has a good understanding of other areas of control an idea of what the field of fuzzy control is concerned with We begin the chapter in Section 5.2 by providing a conventional control engineering perspective on fuzzy control This is essentially a summary of many of the points that we have made throughout the text, but here we bring them all together. Following this, in Section 5.3 we introduce two popular areas in neural networks, the multilayer perceptron and the radial basis function neural network. We explain that a class of radial basis function neural networks is identical to a class of fuzzy systems. Moreover, we explain how techniques covered in this book(e.g, gradient training and adaptive control) can be used for neural networks. In Section 5. 4 we explain genetic algorithms, their relationship to the field of control, and particularly their use with fuzzy systems. Next, in Section 5.5 we provide an overview of some of the relationships to knowledge-based systems, particularly expert systems(and hence expert control) and planning systems
第 5 章 Perspectives on Fuzzy Control 教学内容 本章讲述模糊控制与传统控制的相互关系、模糊神经网络控制、模糊控制和遗传算法的相互联系与区别、 模糊控制与基于知识系统的交叉和融合。 教学重点 重点内容是讲述模糊控制与传统控制的相互关系，模糊系统与神经网络、遗传算法、基于知识的学习系 统的相互联系以及交叉融合。 教学难点 对模糊控制与传统控制、神经网络控制、遗传算法以及基于知识的系统的区别和联系的准确把握和理 解，学会用发展和联系的观点看待智能控制学科的发展。 教学要求 要求学生基本了解模糊控制与传统控制、神经网络控制、遗传算法以及基于知识的系统的区别和联系。 通过本章的学习，进一步加深对智能控制特点的理解，学会用发展和联系的观点看待智能控制学科的发展， 从而培养学生创常新意识和能力，形成正确的工作方法。 5.1 Overview Fuzzy control does not exist as an isolated topic devoid of relationships to other fields, and it is important to understand how it relates to these other fields in order to strengthen your understanding of it. We have emphasized that fuzzy control has its foundations in conventional control and that there are many relationships to techniques, ideas, and methodologies there. Fuzzy control is also an "intelligent control" technique, and hence there are certain relationships between it and other intelligent control methods. In this chapter we will provide a brief overview of some of the basic relationships between fuzzy control and other control methods. This will give the reader who has a good understanding of fuzzy control a glimpse of related topics in other areas. Moreover, it will give the reader who has a good understanding of other areas of control an idea of what the field of fuzzy control is concerned with. We begin the chapter in Section 5.2 by providing a conventional control engineering perspective on fuzzy control. This is essentially a summary of many of the points that we have made throughout the text, but here we bring them all together. Following this, in Section 5.3 we introduce two popular areas in neural networks, the multilayer perceptron and the radial basis function neural network. We explain that a class of radial basis function neural networks is identical to a class of fuzzy systems. Moreover, we explain how techniques covered in this book (e.g., gradient training and adaptive control) can be used for neural networks. In Section 5.4 we explain genetic algorithms, their relationship to the field of control, and particularly their use with fuzzy systems. Next, in Section 5.5 we provide an overview of some of the relationships to knowledge-based systems, particularly expert systems (and hence expert control) and planning systems
Finally, in Section 5.6 we provide an overview of the general area of (hierarchical) intelligent and autonomous control where we offer some ideas on how to define the field of intelligent control and how some of the most general intelligent controllers operate. We use an "intelligent vehicle highway system"problem to illustrate the use of the intelligent autonomous controller functional architecture This chapter is meant to provide a view of, and motivation for, the main areas in the field of intelligent control. The reader interested only in fuzzy control can certainly ignore this chapter; we do not, however, advise this as the relationships to other fields often suggest ideas on how to expand the basic fuzzy control methods and may provide key deas on how to solve a control problem for a particular application 5.2 Fuzzy Versus Conventional Control What are the advantages and disadvantages of fuzzy control as compared to conventional control? What are the perspectives of conventional control engineers on fuzzy control? In this section we will attempt to give answers to these questions by asking, and at least partially answering, a series of questions that we have accumulated over the years from a variety of engineers in industry and universities concerned about whether to use fuzzy or conventional control. We break the questions into three categories and use the questions to summarize several points made in earlier chapters 5.2.1 Modeling Issues and Design Methodology First, we will discuss several issues related to modeling and the overall fuzzy controller design methodology Is the fuzzy controller design methodology viable? Success in a variety of applications (.g, the flexible-link rob application studied in this book)has proven fuzzy control to be a viable methodology and therefore worthy of consideration 2. Do engineers like the methodology? Some do, and some do not. Engineers who have found success with it tend to like it. Often, we find that if engineers invest the time into learning it, they find it to be a tool with which they are comfortable working(they feel like it is"one more tool in their toolbox"). This may be because fuzzy systems are interpolators and engineers are used to thinking about using interpolation as a solution to a wide variety of problems 3. Will the methodology always work? No. The reason we can be so definite in this answer is that it is not the methodology that ultimately leads to success; it is the clever ideas that the control engineer uses to achieve high-performance control. Fuzzy control is a vehicle, and the engineer is the driver. Some find that the vehicle is comfortable and that they can coax it into performing all kinds of functions for them. Others are not so comfortable with 4. Does the design methodology always shorten the"lead time"to design and implementation? In talking with many people in industry, we have found that most often it does(and this is very important, especially in today's competitive climate), but we have also heard of instances where people factor in the cost of having their engineers learn the method and then found the membership functions very hard to tune. In these cases the clear answer from the engineers was that it did not make things easier. We have heard from some that fuzzy logic implements, in a similar way, the standard logic and interpolation methods they already use. Sometimes such engineers find that the fuzzy control jargon clouds the issues that are central to the control problem. Others like that it helps to formalize what they have been doing and helps to suggest ideas for other approaches 5. Is a model used in the fuzzy control design methodology? It is possible that a mathematical model is not used However, often it is used in simulation to redesign a fuzzy controller. Others argue that a model is always used: even if it
Finally, in Section 5.6 we provide an overview of the general area of (hierarchical) intelligent and autonomous control where we offer some ideas on how to define the field of intelligent control and how some of the most general intelligent controllers operate. We use an "intelligent vehicle highway system" problem to illustrate the use of the intelligent autonomous controller functional architecture. This chapter is meant to provide a view of, and motivation for, the main areas in the field of intelligent control. The reader interested only in fuzzy control can certainly ignore this chapter; we do not, however, advise this as the relationships to other fields often suggest ideas on how to expand the basic fuzzy control methods and may provide key ideas on how to solve a control problem for a particular application. 5.2 Fuzzy Versus Conventional Control What are the advantages and disadvantages of fuzzy control as compared to conventional control? What are the perspectives of conventional control engineers on fuzzy control? In this section we will attempt to give answers to these questions by asking, and at least partially answering, a series of questions that we have accumulated over the years from a variety of engineers in industry and universities concerned about whether to use fuzzy or conventional control. We break the questions into three categories and use the questions to summarize several points made in earlier chapters. 5.2.1 Modeling Issues and Design Methodology First, we will discuss several issues related to modeling and the overall fuzzy controller design methodology. 1. Is the fuzzy controller design methodology viable? Success in a variety of applications (e.g., the flexible-link robot application studied in this book) has proven fuzzy control to be a viable methodology and therefore worthy of consideration. 2. Do engineers like the methodology? Some do, and some do not. Engineers who have found success with it tend to like it. Often, we find that if engineers invest the time into learning it, they find it to be a tool with which they are comfortable working (they feel like it is "one more tool in their toolbox"). This may be because fuzzy systems are interpolators and engineers are used to thinking about using interpolation as a solution to a wide variety of problems. 3. Will the methodology always work? No. The reason we can be so definite in this answer is that it is not the methodology that ultimately leads to success; it is the clever ideas that the control engineer uses to achieve high-performance control. Fuzzy control is a vehicle, and the engineer is the driver. Some find that the vehicle is comfortable and that they can coax it into performing all kinds of functions for them. Others are not so comfortable with it. 4. Does the design methodology always shorten the "lead time" to design and implementation? In talking with many people in industry, we have found that most often it does (and this is very important, especially in today's competitive climate), but we have also heard of instances where people factor in the cost of having their engineers learn the method and then found the membership functions very hard to tune. In these cases the clear answer from the engineers was that it did not make things easier. We have heard from some that fuzzy logic implements, in a similar way, the standard logic and interpolation methods they already use. Sometimes such engineers find that the fuzzy control jargon clouds the issues that are central to the control problem. Others like that it helps to formalize what they have been doing and helps to suggest ideas for other approaches. 5. Is a model used in the fuzzy control design methodology? It is possible that a mathematical model is not used. However, often it is used in simulation to redesign a fuzzy controller. Others argue that a model is always used: even if it
is not written down, some type of model is used"in your head. 6. Since most people claim that no formal model is used in the fuzzy control design methodology, the following questions a(a) Is it not true that there are few, if any, assumptions to be violated by fuzzy control and that the technique can be indiscriminately applied? Yes, and sometimes it is applied to systems where it is clear that a Pid controller or look-up table would be just as effective. So, if this is the case, then why not use fuzzy control? Because it is more computationally complex than a Pid controller and the pid controller is much more widely (b) Are heuristics all that are available to perform fuzzy controller design? No. any good models that can be used, probably should be (c) By ignoring a formal model, if it is available, is it not the case that a significant amount of information about how to control the plant is ignored? Yes. If, for example, you have a model of a complex process, we ofter use simulations to gain an understanding of how best to control the plant-and this knowledge can be used to design a fuzzy controller a(d) Can standard control theoretic analysis be used to verify the operation of the resulting control system? Sometimes, if the fuzzy control system satisfies the assumptions needed for the mathematical analysis. This will (e) Will it be difficult to clearly characterize the limitations of various fuzzy control techniques(i.e, to classify which plants can be controlled best with different fuzzy or conventional controllers)? Yes (f) Will it be difficult to clearly relate the results of using the fuzzy controller to previous work in conventional control to definitively show that contributions are being made to the field of control? Yes 7. Is there always a formal model available for control design? No, but for most systems there is at least an approximate model available. This information is often valuable and should not be ignore 8. Does the use of fuzzy controllers limit the design methodology as compared to the use of more general expert controllers? Expert controllers use more general knowledge-representation schemes and inference strategies(see more details in Section 5.5.1), so for some plants it may be advantageous to use the expert controller. It is, however, not clear at this point what class of plants call for the use of expert control 5.2.2 Stability and Performance analysis Next, we will discuss several issues related to the performance analysis of fuzzy control systems 1 Is verification and certification of fuzzy control systems important? Yes, especially for safety-critical systems(e. g an aircraft). It may not be as important for certain applications(e. g, a washing machine with a fuzzy control system) 2. What are the roles of simulation and implementation in evaluating the performance of fuzzy control systems? They lay exactly the same role as for conventional control systems 3. What are the roles of the following nonlinear analysis approaches in fuzzy control system design? (a) Phase plane analy (b) Describing function analysis (c) Stability analysis: Lyapunov's first and second methods; absolute stability; and the small gain theorem (d) Analysis of steady-state errors (e) Method of equivalent gains (f) Cell-to-cell mapping approaches
is not written down, some type of model is used "in your head." 6. Since most people claim that no formal model is used in the fuzzy control design methodology, the following questions arise: (a) Is it not true that there are few, if any, assumptions to be violated by fuzzy control and that the technique can be indiscriminately applied? Yes, and sometimes it is applied to systems where it is clear that a PID controller or look-up table would be just as effective. So, if this is the case, then why not use fuzzy control? Because it is more computationally complex than a PID controller and the PID controller is much more widely understood. (b) Are heuristics all that are available to perform fuzzy controller design? No. Any good models that can be used, probably should be. (c) By ignoring a formal model, if it is available, is it not the case that a significant amount of information about how to control the plant is ignored? Yes. If, for example, you have a model of a complex process, we often use simulations to gain an understanding of how best to control the plant—and this knowledge can be used to design a fuzzy controller. (d) Can standard control theoretic analysis be used to verify the operation of the resulting control system? Sometimes, if the fuzzy control system satisfies the assumptions needed for the mathematical analysis. This will be discussed in more detail in the next section. (e) Will it be difficult to clearly characterize the limitations of various fuzzy control techniques (i.e., to classify which plants can be controlled best with different fuzzy or conventional controllers)? Yes. (f) Will it be difficult to clearly relate the results of using the fuzzy controller to previous work in conventional control to definitively show that contributions are being made to the field of control? Yes. 7. Is there always a formal model available for control design? No, but for most systems there is at least an approximate model available. This information is often valuable and should not be ignored. 8. Does the use of fuzzy controllers limit the design methodology as compared to the use of more general expert controllers? Expert controllers use more general knowledge-representation schemes and inference strategies (see more details in Section 5.5.1), so for some plants it may be advantageous to use the expert controller. It is, however, not clear at this point what class of plants call for the use of expert control. 5.2.2 Stability and Performance Analysis Next, we will discuss several issues related to the performance analysis of fuzzy control systems. 1. Is verification and certification of fuzzy control systems important? Yes, especially for safety-critical systems (e.g., an aircraft). It may not be as important for certain applications (e.g., a washing machine with a fuzzy control system). 2. What are the roles of simulation and implementation in evaluating the performance of fuzzy control systems? They play exactly the same role as for conventional control systems. 3. What are the roles of the following nonlinear analysis approaches in fuzzy control system design? (a) Phase plane analysis. (b) Describing function analysis. (c) Stability analysis: Lyapunov's first and second methods; absolute stability; and the small gain theorem. (d) Analysis of steady-state errors. (e) Method of equivalent gains. (f) Cell-to-cell mapping approaches
Several of these approaches may apply to the analysis of the behavior of the fuzzy control system you design 4. What are the problems with utilizing mathematical analysis for fuzzy control system verification? The techniques take time to learn. The problems for which fuzzy control are particularly well suited, and where there is often very good motivation to use fuzzy rather than conventional control, are the control problems where the plant has complex nonlinear behavior,and where a model is hard to derive due to inherent uncertainties. Each of these characteristics often makes the assumptions that are needed for the nonlinear analysis techniques invalid, so the theory often does not end up offering much when it is really needed 5. Does fuzzy control provide"robust control"? If so, can this be demonstrated mathematically or experimentally? There has been a recent focus in research on stability analysis to show that fuzzy control does provide robust control. It is very difficult, of course, to show robustness via experimentation since by its very definition robustness verification requires extensive experimentation(e.g, you could not call the fuzzy controller for the rotational inverted pendulum case or"robust"when it was only shown to be successful for one disturbance condition) 5.2.3 Implementation and general Issues Finally, we will discuss several issues related to implementation and the overall fuzzy controller design methodology 1. Are there computational advantages in using fuzzy control as compared to conventional control? Not always. PID control is simpler than fuzzy control; however, there are some types of conventional control that are very difficult to implement where a fuzzy controller can be simpler. It depends on the application and the methods you choose 2. Should I use a conventional or"fuzzy processor"for implementation? We have typically found that our needs can be met if we use a conventional processor that has a better track record with reliability; however, there may be some advantages to fuzzy processors when large rule-bases are used and fast sampling times are nee 3. Are there special"tricks of the trade"in the implementation of fuzzy controllers that have many rules? Yes 4. Does fuzzy control provide for a user-friendly way to tune the controller during implementation studies? Often it does. We have found in field studies that when you know generally what to do to get a controller to work, it is sometimes hard to get this information into the gains of a conventional controller and easier to express it in rules and load them into a fuzzy con troller or fuzzy supervisor Overall. in ing fuzzy to conventional control, it is interesting to note that there are conventional control schemes that are analogous to fuzzy ones: (1)direct fuzzy control is analogous to direct nonlinear control, (2)fuzzy adaptive control is analogous to conventional adaptive control (e.g, model reference adaptive control), and (3) fuzzy supervisory control is analogous to hierarchical control. Does there exist an analogous conventional approach to every the performance of the fuzzy versus the convent ona approach it seems to be very important to compare and contrast 5.3 Neural Networks Artificial neural networks are circuits, computer algorithms, or mathematical representations of the massively connected set of neurons that form biological neural networks. They have been shown to be useful as an alternative computing echnology and have proven useful in a variety of pattern recognition, signal processing, estimation, and control problems. Their capabilities to learn from examples have been particularly useful In this section we will introduce two of the more popular neural networks and discuss how they relate to the areas of uzzy systems and control. We must emphasize that there are many topics in the area of neural networks that are not
Several of these approaches may apply to the analysis of the behavior of the fuzzy control system you design. 4. What are the problems with utilizing mathematical analysis for fuzzy control system verification? The techniques take time to learn. The problems for which fuzzy control are particularly well suited, and where there is often very good motivation to use fuzzy rather than conventional control, are the control problems where the plant has complex nonlinear behavior, and where a model is hard to derive due to inherent uncertainties. Each of these characteristics often makes the assumptions that are needed for the nonlinear analysis techniques invalid, so the theory often does not end up offering much when it is really needed. 5. Does fuzzy control provide "robust control"? If so, can this be demonstrated mathematically or experimentally? There has been a recent focus in research on stability analysis to show that fuzzy control does provide robust control. It is very difficult, of course, to show robustness via experimentation since by its very definition robustness verification requires extensive experimentation (e.g., you could not call the fuzzy controller for the rotational inverted pendulum case or "robust" when it was only shown to be successful for one disturbance condition). 5.2.3 Implementation and General Issues Finally, we will discuss several issues related to implementation and the overall fuzzy controller design methodology. 1. Are there computational advantages in using fuzzy control as compared to conventional control? Not always. PID control is simpler than fuzzy control; however, there are some types of conventional control that are very difficult to implement where a fuzzy controller can be simpler. It depends on the application and the methods you choose. 2. Should I use a conventional or "fuzzy processor" for implementation? We have typically found that our needs can be met if we use a conventional processor that has a better track record with reliability; however, there may be some advantages to fuzzy processors when large rule-bases are used and fast sampling times are needed. 3. Are there special "tricks of the trade" in the implementation of fuzzy controllers that have many rules? Yes. 4. Does fuzzy control provide for a user-friendly way to tune the controller during implementation studies? Often it does. We have found in field studies that when you know generally what to do to get a controller to work, it is sometimes hard to get this information into the gains of a conventional controller and easier to express it in rules and load them into a fuzzy controller or fuzzy supervisor. Overall, in comparing fuzzy to conventional control, it is interesting to note that there are conventional control schemes that are analogous to fuzzy ones: (1) direct fuzzy control is analogous to direct nonlinear control, (2) fuzzy adaptive control is analogous to conventional adaptive control (e.g., model reference adaptive control), and (3) fuzzy supervisory control is analogous to hierarchical control. Does there exist an analogous conventional approach to every fuzzy control scheme? If so, then in doing fuzzy control research it seems to be very important to compare and contrast the performance of the fuzzy versus the conventional approaches. 5.3 Neural Networks Artificial neural networks are circuits, computer algorithms, or mathematical representations of the massively connected set of neurons that form biological neural networks. They have been shown to be useful as an alternative computing technology and have proven useful in a variety of pattern recognition, signal processing, estimation, and control problems. Their capabilities to learn from examples have been particularly useful. In this section we will introduce two of the more popular neural networks and discuss how they relate to the areas of fuzzy systems and control. We must emphasize that there are many topics in the area of neural networks that are not
covered here. For instance, we do not discuss associative memories and Hopfield neural networks, recurrent networks Boltz-mann machines, or Hebbian or competitive learning. We refer the reader to Section 5.8, For Further Study, for references that cover these topics in detail 5.3.1 Multilayer Perceptrons The multilayer perceptron is a feed-forward neural network (i.e, it does not use past values of its outputs or other internal variables to compute its current output). It is composed of an interconnection of basic neuron processing units The Neuron For a single neuron, suppose that we use, i=1, 2, , n, to denote its inputs and suppose that it has a single output y Figure 5. 1 shows the neuron. Such a neuron first forms a weighted sum of the inputs 2nx|- wherea are the interconnection"weights"andes the"bias"for the neuron(these parameters model the interconnections between the cell bodies in the neurons of a biological neural network ). The signal represents a signal in the biological neuron, and the processing that the neuron performs on this signal is represented with an"activation function. This activation function is represented with a function f, and the output that it computes y=f(-)=川mx-0 (5.1) Basically, the neuron model represents the biological neuron that"fires"(turns on) when its inputs are significantly excited (ie, is big enough). The manner in which the neuron fires is defined by the activation function f. There are many ways to define the activation function Threshold function: For this type of activation function we have if f( 0 if 2<0 so that once the input signal is above zero the neuron turns on a Sigmoid function: For this type of activation function we have f(=)=1+eXp(-bx) so that the input signal continuously turns on the neuron an increasing amount as it increases(plot the function values against z to convince yourself of this). The parameter b affects the slope of the sigmoid function. There are many functions that take on a shape that is sigmoidal. For instance, one that is often used in neural network is the hyperbolic tangent function f(a)=tanh(-) 1-exp(=) 21+exp() Equation(5.1), with one of the above activation functions, represents the computations made by one neuron in the neural network. Next, we define how we interconnect these neurons to form a neural network-in particular, the multilayer perceptron
covered here. For instance, we do not discuss associative memories and Hopfield neural networks, recurrent networks, Boltz-mann machines, or Hebbian or competitive learning. We refer the reader to Section 5.8, For Further Study, for references that cover these topics in detail. 5.3.1 Multilayer Perceptrons The multilayer perceptron is a feed-forward neural network (i.e., it does not use past values of its outputs or other internal variables to compute its current output). It is composed of an interconnection of basic neuron processing units. The Neuron For a single neuron, suppose that we use , i = 1,2,..., n, to denote its inputs and suppose that it has a single output y. Figure 5.1 shows the neuron. Such a neuron first forms a weighted sum of the inputs 1 n i i i z x ω θ = ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ ∑ whereωi are the interconnection "weights" andθis the "bias" for the neuron (these parameters model the interconnections between the cell bodies in the neurons of a biological neural network). The signal z represents a signal in the biological neuron, and the processing that the neuron performs on this signal is represented with an "activation function." This activation function is represented with a function f, and the output that it computes is ( ) 1 n i i i y fz f x ω θ = ⎛ ⎞ ⎛ ⎞ == − ⎜⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ∑ ⎟ ( 5.1) Basically, the neuron model represents the biological neuron that "fires" (turns on) when its inputs are significantly excited (i.e., z is big enough). The manner in which the neuron fires is defined by the activation function f . There are many ways to define the activation function: Threshold function: For this type of activation function we have ( ) 1 if 0 0 if 0 z f z z ⎧ ≥ = ⎨ ⎩ < so that once the input signal z is above zero the neuron turns on. Sigmoid function: For this type of activation function we have 1 ( ) 1 exp( ) f z bz = + − (5.2) so that the input signal z continuously turns on the neuron an increasing amount as it increases (plot the function values against z to convince yourself of this).The parameter b affects the slope of the sigmoid function. There are many functions that take on a shape that is sigmoidal. For instance, one that is often used in neural networks is the hyperbolic tangent function 1 exp( ) ( ) tanh( ) 2 1 exp( ) z z f z z − = = + Equation (5.1), with one of the above activation functions, represents the computations made by one neuron in the neural network. Next, we define how we interconnect these neurons to form a neural network—in particular, the multilayer perceptron