Neural network modeling inverse

A. P. d. Weijer, C. B. Lucasius, L. Buydens, and G. Kateman, Chemometrics Intell. Lab. Syst., 20, 45 (1993). Using Genetic Algorithms for an Artificial Neural Network Model Inversion. 

Internal Model Control was diseussed in relation to robust eontrol in seetion 9.6.3 and Figure 9.19. The IMC strueture is also applieable to neural network eontrol. The plant model GmC) in Figure 9.19 is replaeed by a neural network model and the eontroller C(.v) by an inverse neural network plant model as shown in Figure 10.30. 

Figure 12.3 Direct neural network modeling (a) and inverse neural network modeling (b) for free radical polymerization of MMA.

S. Curteanu, Direct and inverse neural network modeling in free radical polymerization. Cent. Eur. J. Chem., 2 (1), 113-140,2004. 

Lobato J, Canizares P, Rodrigo MA et al (2010) Direct and inverse neural networks modelling applied to study the influence of the gas diffusion layer properties on PBI-based PEM fuel cells. Int J Hydrogen Energy 35 7889-7897... 

Figure 3. Inverse neural network model proposed...

N. Aziz, M.A. Hussain, I.M. Mujtaba, Optimal control of batch reactor comparison of neural network based GMC and inverse model control approach, in Proceedings of the Sixth World Congress of Chemical Engineering, Melbourne, Australia, 23-27 September 2001. 

Relationships among manipulated (controlled) variables, online measured variables, and product (uncontrolled) variables in most biosystems are nonlinear to some extent [95]. A forward model is when parameters, starting conditions, and relevant equations governing behavior are known, readily measurable inputs and the outputs are variables an inverse model is when the inputs are readily measurable variables and the outputs are difficult to measure parameters [69]. The forward model is most applicable to process validation, whereas the inverse model is most applicable to metabolic pathway analysis. Modeling systems such as neural networks have been used to describe the characteristics of extremely complex bioprocess systems [95]. 

In direct inverse control, (Figure 12.2), the neural network is used to compute an inverse model of the system to be controlled ]Levin et al., 1991 Nordgren and Meckl, 1993]. In classical linear control techniques, one would find a linear model of the system then analytically compute the inverse model. Using neural networks, the network is trained to perform the inverse model calculations, that is, to map system outputs to system inputs. Biomedical applications of this type of approach include the control of arm movements using electrical stimulation [Lan et al., 1994] and the adaptive control of arterial blood pressure [Chen et al, 1997]. 

The total control effort u appHed to the plant is the sum of the feedback control output and network control output. The ideal configuration of the neural network would correspond to the inverse mathematical model of the system s plant. The network is given information of the desired position and its derivatives, and it will calculate the control effort necessary to make the output of the system foUow the desired trajectory. If there are no disturbances the system error will be zero. 

In essence, the output of the feedback controller is an indication of the mismatch between the dynamics of the plant and the inverse-dynamics model obtained by the neural network. If the true inverse-dynamic model has been learned, the neural network alone wiU provide the necessary control signal to achieve the desired trajectory [118,120],... 

Various neural network-based adaptive control techniques were discussed in this study. A major problem in implementing neural network-based MRACs is the translation of the output error between the plant and the reference model so as to train the neural controller. A technique called iterative inversion, which inverts the neural identification model of the plant for calculating neural controller gains, has been used. Due to the real-time computer hardware limitations, the performance of neural network-based adaptive control systems is verified using simulation studies only. These results show that neural-network based MRACs can be designed and implemented on smart structures. 

Learning involves thus designating the miiumum of the error function. For this purpose, we usually apply gradient methods (conjugate gradients), based on the Hessian matrix (Newton, Levenberg-Marquardt methods), or on approximation of the inverse of the Hessian matrix (quasi-Newton methods) [2]. The MLP neural network is sensu stricte a static model, but it is possible to introduce dynamics... 

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