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 adaptive /e control 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
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
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
n 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
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
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
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 gure 8. 1 shows the neuron Such a neuron first forms a weighted sum of the inputs =1 where w; are the interconnection weights and eis 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 y=f(=)=f nx)-a)(51)
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 8.1 shows the neuron. Such a neuron first forms a weighted sum of the inputs where ωi are the interconnection "weights" and θis 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 ( 5.1) 1 n i i i z x = = − ( ) 1 n i i i y f z f x = = = −