Adaptive wavelet control of nonlinear systems

Polycarpou, Marios M.; Mears, Mark J.; Weaver, S.E.

doi:10.1109/cdc.1997.652469

Cited by 19 publications

(7 citation statements)

References 18 publications

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“…It is more convenient in practice to use a redundant wavelet family than an orthonormal wavelet basis for constructing the wavelet network, because admitting redundancy allows us to construct wavelet functions with a simple analytical form and good spatial-spectral localization properties [5]. In this paper, a nonorthogonal wavelet has been used as a mother wavelet which is the first derivative of a Gaussian function as shown in (14).…”

Section: Mother Wavelet Functionmentioning

confidence: 98%

“…The optimal wavelet network structure is achieved the best approximation and prediction capability [17]. Wavelets show local characteristics which is the main property in both space and spatial frequency [14]. Therefore, among the all input scope of the network, the hidden nodes with the wavelet function influence the networks output only in some local range.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet networks for nonlinear system modeling

Postalcioglu

Becerikli

2006

Neural Comput & Applic

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This study presents a nonlinear systems and function learning by using wavelet network. Wavelet networks are as neural network for training and structural approach. But, training algorithms of wavelet networks is required a smaller number of iterations when the compared with neural networks. Gaussianbased mother wavelet function is used as an activation function. Wavelet networks have three main parameters; dilation, translation, and connection parameters (weights). Initial values of these parameters are randomly selected. They are optimized during training (learning) phase. Because of random selection of all initial values, it may not be suitable for process modeling. Because wavelet functions are rapidly vanishing functions. For this reason heuristic procedure has been used. In this study serial-parallel identification model has been applied to system modeling. This structure does not utilize feedback. Real system outputs have been exercised for prediction of the future system outputs. So that stability and approximation of the network is guaranteed. Gradient methods have been applied for parameters updating with momentum term. Quadratic cost function is used for error minimization. Three example problems have been examined in the simulation. They are static nonlinear functions and discrete dynamic nonlinear system.

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Section: Mother Wavelet Functionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Wavelet networks for nonlinear system modeling

Postalcioglu

Becerikli

2006

Neural Comput & Applic

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“…The first derivative of a gaussian wavelet is used as the transfer function for wavenet. Wavelets show local characteristics [7,12]. Fig.…”

Section: Introductionmentioning

confidence: 98%

Comparison of Wavenet and Neuralnet for System Modeling

Postalcioglu

Erkan

Bolat

2005

Lecture Notes in Computer Science

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Abstract. This paper presents nonlinear static and dynamic system modeling using wavenet and neuralnet. Wavenet combines wavelet theory and feedforward neuralnet, so learning approach is similar to neuralnet. The selection of transfer function is crucial for the approximation property and the convergence of the network. The purelin and the tansig functions are used as the transfer functions for neuralnet and the first derivative of a gaussian function is used as the transfer function for wavenet. Wavenet and neuralnet parameters are optimized during learning phase. Selecting all initial values random, but for wavenet, it may be unsuitable for process modeling because wavelets have localization feature. For this reason heuristic procedure has been used for wavenet. In this study gradient methods have been applied for parameters updating with momentum. Error minimization is computed by quadratic cost function for wavenet and neuralnet. Nonlinear static and dynamic functions have been used for the simulations. Recently wavenet has been used as an alternative of the neuralnet because interpretation of the model with neuralnet is so hard. For wavenet learning approach, training algorithms require smaller number of iterations when compared with neuralnet. Consequently, according to the number of training iteration and TMSE, dynamic and static system modeling with wavenet is better as shown in results.

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“…There are lots of works about this application in the controller design of uncertain nonlinear systems [8][9][10][11]. In [9], an adaptive learning control approach based on wavelet was presented for a class of uncertain nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

On-line approximation based robust adaptive control for a class of uncertain systems

Wang

Peng

et al. 2010

2010 8th World Congress on Intelligent Control and Automation

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Three kinds of approximators are widely used in adaptive controllers for the nonlinear systems with uncertainty. They are neural network, fuzzy logic systems and wavelet approximator, respectively. By unifying these three approximators, we developed an on-line approximation based controller for a class of uncertain nonlinear systems. It is proved that with the proposed control law and update laws, the closed-loop system is guaranteed to be stable and the tracking error converges to zero in the presence of unknown nonlinearity. A simulation example is presented to demonstrate the method.Index Terms-on-line approximator; neural network; fuzzy logic systems; wavelet; nonlinear systems

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Adaptive wavelet control of nonlinear systems

Cited by 19 publications

References 18 publications

Wavelet networks for nonlinear system modeling

Wavelet networks for nonlinear system modeling

Comparison of Wavenet and Neuralnet for System Modeling

On-line approximation based robust adaptive control for a class of uncertain systems

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