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NDL India: Strategies for Feedback Linearisation: A Dynamic Neural Network Approach
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Strategies for Feedback Linearisation
In most cases authors are permitted to post their version of the article e. The development of novel DNN structures, which has good mapping capability, is a relevant challenge being addressed in this paper. Although the structure Keywords: is changed minorly only, the mapping capability of the new designed DNN in this paper has been Recurrent neural networks improved dramatically. Previous work [J. Deng et al. This type of DNNs does not require the output of the plant to be used as an input to the model. To illustrate the capabilities of the new structure, neural networks are trained to identify a real nonlinear 3D crane system.
All rights reserved. A linear controller can be applied to the linearised Narendra and Parthasarathy, ; Miller et al. The main draw- industrial control systems exhibit nonlinear characteristics. Most back of the input—output linearisation technique is that it conventional control schemes use linear models. However, the depends on the exact knowledge of a nonlinear model of the use of linear models can result in a serious deterioration of process.
The presence of this may be overcome by using a dynamic neural network to nonlinearities in control systems complicates the design stages identify a model to be suitable for the input—output linearisation and may cause performance problems if not considered appro- and decoupling. A recurrent neural network is a closed loop priately. Research over decades has produced several nonlinear system, with feedback paths introducing dynamics into the control strategies based on mathematical foundations.
One of the model. They can be trained to learn the system dynamics without most important control techniques is the input—output linearisa- assuming much knowledge about the structure of the system tion of nonlinear systems. Based on differential geometric con- under consideration. E-mail address: jiameideng hotmail. An state of the n output units. Although the uses the whole state vector of the network, which consists of the structure is changed minorly only, the mapping capability of the output states and the hidden states, in the argument of the vector new designed DNN in this paper has been improved dramatically.
The difference is illustrated in Figs. A type 3 DNN is different from a given. To illustrate the capabilities of the new structure, neural type 1 DNN in that a type 3 DNN uses the outputs from another networks are trained to identify a real nonlinear 3D crane system. Section 3 introduces the class of dynamic neural networks consists of the output states and the hidden states, in the of interest in this paper. Section 4 discusses theoretical results on argument of the vector sigmoid function. The type 3 DNN is the approximation ability of dynamic neural networks.
Section 5 illustrated in Fig. Finally, Section 6 gives concluding remarks. Different types of dynamic neural networks Dynamic neural networks are made of interconnected dynamic neurons, also called units. A dynamic neural network is formed by a single layer of N units. Block diagram of type 1 DNN. A type 1 DNN differs from the dynamic neural network described in Chapter 4 of the book Garces et al. Block diagram of type 2 DNN. Author's personal copy J. Block diagram of type 3 DNN. The book Garces provided that the number of units in the hidden layer is et al.
This is stated by the following theorem, approximate general nonlinear systems. Let K be a compact set of Rn and f : K-Rq be a dimensional vector b such that continuous mapping. Let D be an open subset of Rn , and U an open subset of Rm. Then, for an arbitrary e 4 0, there exists a non-autonomous dynamic neural network with n output units with 4.
See the book Garces et al. Theorem 4. For given e1 4 0, choose e 4 0, e2 40 and such that which completes the proof. This proof is similar to Theorem 4 and uses Lemmas 1—3, dz.
Sigmoid function is a continuous and differentiable function. Let lG is the Lipschitz constant of F in z.
Related Strategies for Feedback Linearisation: A Dynamic Neural Network Approach
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