Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.
This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.
Department of Power and Control Engineering, School of Electrical and Computer Engineering, Shiraz University, P.O.box 7134851154, Shiraz, Iran. Electronic address: jafarim@shirazu.ac.ir.
Masoumeh
M
Jafari
School of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran. Electronic address: msalimifard@aut.ac.ir.
Maryam
M
Salimifard
Department of Power and Control Engineering, School of Electrical and Computer Engineering, Shiraz University, P.O.box 7134851154, Shiraz, Iran. Electronic address: mdehghani@shirazu.ac.ir.
Maryam
M
Dehghani
Colored noises; Hammerstein model; Multi-input multi-output systems; Nonlinear systems; System identification; Wiener model