Abstract
This paper considers the identification of nonlinear systems with color noise, and introduces a new time-varying forgetting factor based stochastic gradient (TVFF-SG) algorithm to estimate the system parameters. The basic idea of the time-varying forgetting factor is that when the algorithm starts, we give the forgetting factor a relative smaller value, which will speed up the convergence. In addition, the forgetting factor will increase slowly as time goes on so that the convergence procedure of the model will be more stable. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.
Highlights
System identification aims to build a mathematical model from data generated by a dynamical system
In the past several decades, a variety of types of reliable system identification algorithms have been proposed such as bayesian method [10], stochastic gradient method [11], least squares method [12], Newton iterative method [13], evolutionary optimization based method [14] and so on
When the forgetting factor is small, the stability of the algorithm will be reduced. To solve this problem, we propose a new time-varying forgetting factor stochastic gradient algorithm to estimate the system parameters
Summary
System identification aims to build a mathematical model from data generated by a dynamical system. System identification is a powerful technique which has great potential in many applied areas such as model-based simulation, prediction and control of dynamical systems[1,2,3,4,5]. In order to solve this problem, forgetting factor stochastic gradient(FF-SG) algorithm was proposed[18,19,20]. When considering the forgetting factor, an important idea is to make a tradeoff between the convergence rate and the stability of convergence. Based on this idea, the researchers seek to apply variable forgetting factors for solving the parameter identification problems. A time-varying forgetting factor stochastic gradient algorithm is proposed to identify the parameters of nonlinear systems with color noise
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