State space neural network. Properties and application

In this paper, a specific neural network based model for the identification of non-linear systems is proposed. This neural network structure is able to identify a state space non-linear model of the plant. The use of the state space representation presents several advantages that must be taken into account. One of the most important advantages is that the resulting neural model can be easily linearized around different operating points, allowing application of classical stability theorems from the linear systems domain to this class of neural networks. In this way, some useful theoretical results for neural modelling and identification have been obtained and presented in the paper. In this paper, several stability theorems and practical implementation issues are addressed. Examples are also presented which show the training capability of the neural network and the validity of the theory presented.

[1]  Stefen Hui,et al.  Application of feedforward neural networks to dynamical system identification and control , 1993, IEEE Trans. Control. Syst. Technol..

[2]  Bernard Widrow,et al.  30 years of adaptive neural networks: perceptron, Madaline, and backpropagation , 1990, Proc. IEEE.

[3]  Jaap Hoekstra,et al.  Recurrence with Delayed Links in Multilayer Networks for Processing Sequential Data , 1991 .

[4]  Norio Baba,et al.  A new approach for finding the global minimum of error function of neural networks , 1989, Neural Networks.

[5]  C. De Prada,et al.  Identification and constrained multivariable predictive control of chemical reactors , 1995, Proceedings of International Conference on Control Applications.

[6]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[7]  Ronald J. Williams,et al.  Adaptive state representation and estimation using recurrent connectionist networks , 1990 .

[8]  Amir F. Atiya,et al.  Application of the recurrent multilayer perceptron in modeling complex process dynamics , 1994, IEEE Trans. Neural Networks.

[9]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[10]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[11]  Peter J. Gawthrop,et al.  Neural networks for control systems - A survey , 1992, Autom..

[12]  W. D. Ray.  Matrices in control theory , 1984 .

[13]  N. V. Bhat,et al.  Use of neural nets for dynamic modeling and control of chemical process systems , 1990 .

[14]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[15]  W. Richard Kolk,et al.  Nonlinear System Dynamics , 1992 .

[16]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[17]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[18]  Patrick van der Smagt.  Minimisation methods for training feedforward neural networks , 1994, Neural Networks.

[19]  K. Warwick,et al.  Dynamic recurrent neural network for system identification and control , 1995 .

[20]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.