International Journal of Computational Intelligence Volume 1 Number 2
Fuzzy Wavelet Neural Network for Control of Dynamic Plants Rahib Hidayat Abiyev
Abstract- The development of control system for the dynamic processes characterizing uncertainties needs the creating of the proper knowledge base for the controller. In this paper, to solve this problem the integration of fuzzy set theory and wavelet neural network (WNN) is considered. The structure and operation algorithms of fuzzy WNN based controller are presented. Using gradient method the learning of fuzzy WNN is performed to find optimal values of the parameters of controller. The simulation of fuzzy WNN based control system for control of dynamic plant is carried out. Result of simulation of control system based on fuzzy WNN is compared with the simulation result of control systems based on feedforward neural network and PID controller. Simulation results demonstrate that training of fuzzy WNN based control system is faster and it has better control performance than others.
Keywords- Wavelet neural network, Fuzzy wavelet, Fuzzy wavelet neural network based controller I. INTRODUCTION
I
N industry some technological processes are characterized by unpredictable and hard formalized factors, uncertainty, fuzziness of information. In these situation deterministic models is not enough adequately describe these processes and control on the base of these models begun difficult. In these conditions it is advisable to use fuzzy technology, neural networks which provide adequacy of the model and independency of the model to disturbance. Fuzzy technology is effective tool for dealing with complex, nonlinear processes characterizing with ill-defined and uncertainty factors. One of majority application of fuzzy logic is control. Fuzzy controller model is based on constructing knowledge base which is created on the base of knowledge of human experts. The constructing of knowledge base for some complicated processes is difficult. In most cases these knowledge base consists of IF-Then linguistic rules. There are different ways for constructing of fuzzy rules. In this paper for constructing of fuzzy rules the wavelet neural network is used. The use of wavelet neural networks allows fuzzy system to learn a certain function, which is highly nonlinear, represent dynamic of the processes. This is performed during training period of controllers. In recent years the development of controllers on the base neural networks has been paid much attention. The key factors
for their use in the control field are properties that they have. These properties are learning and generalization abilities, nonlinear mapping, parallelism of computation, vitality. Due to these characteristics neural network becomes great of importance for application in such areas as artificial behavior, artificial intelligence, theory of control and decision making, identification, optimal control, robotics etc. The learning capabilities of neural network allows controller to learn a certain function, which are highly nonlinear, represent dynamic of the processes. This is performed during long training period of controllers in supervised and unsupervised manner. There are different neural network structures. One of type is wavelet NN that use wavelet functions. A wavelet networks are nonlinear regression structure that represents input-output mappings. The network based on wavelet has simple structure and good learning speed. It can converge faster and more adaptive to new data. Wavelet neural networks use basis functions in hidden layer. They can approximate complex functions to some precision very compactly and can be easily designed and trained than other networks, such as multilayer perceptrons and radial based networks [1-3]. A good initialization of wavelet neural networks allows to obtain fast convergence. Number of methods is implemented for initializing wavelets, such as orthogonal least square procedure, clustering method [1]. The optimal dilation of the wavelet increases training speed and obtains fast convergence. The combination of wavelet network and fuzzy logic allow to develop system that have fast training speed, describe nonlinear objects that are characterized uncertainty. In the paper using fuzzy wavelet neural network the development of controller is considered. II. WAVELET NEURAL NETWORK Wavelet networks use three-layer structure and wavelet activation function. Wavelet function is a waveform that has limited duration and average value of zero. There are number of wavelet functions. In this work the Mexican Hat wavelet is used for neural network.
\ ( z ) D (1 z 2 ) * e Here D
Manuscript received July, 2003. This work was supported by the Near East University, Lefkosha, TRNC, Turkey. Rahib H. Abiyev is with the Department of Computer Engineering, Near East University, Mersin-10, TRNC, Turkey (e-mail:
[email protected]).
2 3
z2 2
S 1 / 4 . The outputs of hidden neurons of
network are computed by equation (1). The structure of wavelet network is given in figure 1.
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(1)
International Journal of Computational Intelligence Volume 1 Number 2
be used. During learning the parameters of the network are optimized.
Here x1, x2, …, xn are network input signals.
