论文信息 - Non-integer order integration by using neural networks

Non-integer order integration by using neural networks

In this paper a new method for non-integer order integration is presented. It is based on a Multi-layer Perceptron modelization that allows an easy circuit design and a wide range of integration order. The neural network approach allows one to overcome some problems related to practical implementation of the circuit. An example of application regarding the control of a chaotic system is also reported in order to validate the proposed neural network modeling technique.

[1] C. F. Lorenzo,et al. Chaos in a fractional order Chua's system , 1995 .

[2] M. S. Keshner. 1/f noise , 1982, Proceedings of the IEEE.

[3] P. Arena,et al. Bifurcation and Chaos in Noninteger Order Cellular Neural Networks , 1998 .

[4] K. B. Oldham,et al. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[5] B. Onaral,et al. Fractal system as represented by singularity function , 1992 .

[6] I. Podlubny. Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[7] Richard S. Sutton,et al. Neural networks for control , 1990 .

[8] Liu. Fractal model for the ac response of a rough interface. , 1985, Physical review letters.

[9] Igor Podlubny,et al. Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[10] T. Roska,et al. Dynamics of the Lorenz equation and Chua's equation: a Tutorial , 1993, Chua's Circuit.

[11] A. Oustaloup. Systèmes asservis linéaires d'ordre fractionnaire : théorie et pratique , 1983 .

[12] B. Onaral,et al. Time domain characteristics of rational systems with scale-invariant frequency response , 1996, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications.

[13] B. Ross,et al. Fractional Calculus and Its Applications , 1975 .