الگوریتم یادگیری برای سیستم های دینامیکی
Abstract
1-Introduction
2-Fractional Calculus
3-Problem statement
4-Stochastic Gradient Algorithm for Learning a Fractional-Order Dynamical System with Autocorrelated Error- in-Variables
5-Stochastic Approximation with Averaging
6-Simulation Results
7-Conclusion
References
Abstract
In this paper, the stochastic gradient algorithm for learning fractional-order dynamical systems with noisy input and output is proposed. The proposed algorithm allows estimating the parameters of fractional dynamic systems if the input and output noises are color. The proposed algorithm does not require knowledge of the noise distribution laws. The simulation results demonstrate the high accuracy of the proposed learning algorithm in comparison with the least squares learning algorithm.
Introduction
Instrumental variables for fractional systems with correlated noise are presented in Victor et al., 2011 Recursive identification algorithms for white noise are proposed in Djouambi, 2012. The use of Kalman filter for white noise in Sierociuk, Dzienlinsk, 2006 and color noise in Sierociuk, Zubinski, 2014, Safarinejadian et al., 2016, Yang et al., 2018 is considered. An excellent review of methods for identifying integer-order systems with errors in variables is given in Söderström. 2018. Today there are a small number of articles on the identification of fractional systems with errors in variables Chetoui et al., 2012, Chetoui et al., 2013, Ivanov, 2013. In Ivanov, 2017 proposed a generalization of the results for the case of fractional errors in variables.