1. Background on Neural Networks and Fuzzy Logic Systems
Society for Industrial and Applied Mathematics eBooks · 2002
In this chapter, we provide a brief background on neural networks (NNs) and fuzzy logic (FL) systems, covering the topics that will be needed for control system design using these techniques. Included are NN and FL system structures, learning, and the approximation property. We present different types of NN systems and show how NNs and FL systems are related. In fact, FL systems are NNs with a special structure. Both NNs and FL systems belong to a larger class of systems called nonlinear network structures (Lewis (1999)) that have some properties of extreme importance for feedback control systems. These are made up of multiple interconnected nodes and can learn by modifying the weights interconnecting the nodes. This process is called tuning the weights. Changing the weights changes the knowledge stored in the network; in fact, the values of the weights represent the memory of the network. NNs are a special sort of nonlinear network that are modeled on the nervous systems of biological systems. FL systems are a special sort that are modeled after the linguistic and reasoning abilities of humans. It is fascinating that there are such close connections between these two sorts of nonlinear networks, as we reveal in this chapter. 1.1 Neural networks NNs (Haykin (1994), Kosko (1992)) are closely modeled on biological processes for information processing, specifically the nervous system and its basic unit, the neuron. The neuron receives multiple signals from other neurons through its dendrites, each signal multiplied by a weighting coefficient. These signals are added in the cell body or soma, and when the composite signal reaches a threshold value, a signal known as the action potential is sent through the axon, which is the neuron's output channel. More detail on the material in this chapter may be found in Lewis, Jagannathan, and Yesildirek (1999). 1.1.1 Two-layer neural network topology and tuning A mathematical model of an NN is shown in Figure 1.1.1. This NN has two layers of adjustable weights and is known as a two-layer NN. The values xk are the NN inputs and yi its outputs. Function σ(.) is a nonlinear activation function contained in the hidden layer (the middle layer of nodes) of the NN.