A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems

Za'Er Abo-Hammour,Shaher Momani,Othman Alsmadi,Omar Abu Arqub

doi:10.1155/2013/831657

Abstract

Modelling of linear dynamical systems is very important issue in science and engineering. The modelling process might be achieved by either the application of the governing laws describing the process or by using the input-output data sequence of the process. Most of the modelling algorithms reported in the literature focus on either determining the order or estimating the model parameters. In this paper, the authors present a new method for modelling. Given the input-output data sequence of the model in the absence of any information about the order, the correct order of the model as well as the correct parameters is determined simultaneously using genetic algorithm. The algorithm used in this paper has several advantages; first, it does not use complex mathematical procedures in detecting the order and the parameters; second, it can be used for low as well as high order systems; third, it can be applied to any linear dynamical system including the autoregressive, moving-average, and autoregressive moving-average models; fourth, it determines the order and the parameters in a simultaneous manner with a very high accuracy. Results presented in this paper show the potentiality, the generality, and the superiority of our method as compared with other well-known methods.

Highlights

Modelling of linear dynamical systems is encountered in many fields including financial markets, environmental sciences, control engineering, and many other fields (Zivot and Wang [1], Landau and Zito [2])
In a Genetic algorithm (GA), a fitness function is used to evaluate the degree of goodness of a chromosome
Where MSE is mean square error obtained based on the true system output and the estimated GA model output

Summary

Introduction

Modelling of linear dynamical systems is encountered in many fields including financial markets, environmental sciences, control engineering, and many other fields (Zivot and Wang [1], Landau and Zito [2]). The modelling process can be achieved using one of two main scenarios: the first scenario is based on the complete understanding of the physical process that leads to the derivation of the governing differential equations describing the process. In this case, the model might be fully known in terms of the order and the parameters or might be partially known where some or all of the parameters are unknown. Modelling of linear dynamical systems leads to either a transfer function or a state space representation (Landau and Zito [2], Garcia-Hiernaux et al [3]). The previous models play an important role in system identification and have a wide range of applications such as communication, signal processing, control systems, biomedical engineering, image processing and compression, prediction of spectrum estimation, and controlling of dynamic systems (Fenga and Politis [7], Broersen and deWaele [8])

Methods

Results

Discussion

Conclusion