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 notSeveral 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