Decomposition and composition modeling algorithms for control systems with colored noises

Abstract

SummaryThis article proposes a novel identification framework for estimating the parameters of the controlled autoregressive autoregressive moving average (CARARMA) models with colored noise. By means of building an auxiliary model and using the hierarchical identification principle, this article investigates a highly‐efficient parameter estimation algorithm. In order to meet the need for identifying the systems with large‐scale parameters, the whole parameters of the CARARMA system is separated into two parameter sets and a decomposition and composition recursive identification algorithm (i.e., hierarchical generalized extended least squares algorithm or decomposition‐based recursive generalized extended least squares algorithm) is presented. Moreover, this article analyzes the convergence of the proposed decomposition and composition recursive identification algorithm. The performance analysis shows that the proposed decomposition and composition identification algorithm can reduce the complexity of the identification algorithm compared with the algorithm without decomposition.

Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

“…The proposed parameter estimation algorithms in this article can combine other identification algorithms [78][79][80][81][82][83] to explore new parameter estimation methods of different dynamic stochastic systems [84][85][86][87][88][89] and can be applied to signal processing and chemical process control. [90][91][92][93][94][95][96] The steps of computing the P-REG parameter estimation vector θ(t) in ( 19)-( 26) are listed in the following.…”

Online identification of Hammerstein systems with B‐spline networks

“…The reason why the BS‐MDWSG algorithm can improve the estimation accuracy is that it updates $$$ {\hat{\boldsymbol{\theta}}}_{s1}\left(t-1\right) $$$ and $$$ \hat{\boldsymbol{w}}\left(t-1\right) $$$ using data block by block based a moving data window and the window length is determined by $$$ m $$$ value. The proposed parameter identification algorithms in this article can combine other parameter estimation algorithms 69–74 to explore new parameter estimation methods of different dynamic stochastic systems 75–80 and can be applied to signal processing and chemical process control 81–86 …”