Title :
Recursive Identification of MIMO Wiener Systems
Author :
Bi-Qiang Mu ; Han-Fu Chen
Author_Institution :
Key Lab. of Syst. & Control, Acad. of Math. & Syst. Sci., Beijing, China
Abstract :
Stochastic approximation (SA) algorithms are proposed to identify a multi-input and multi-output (MIMO) Wiener system, in which the system input is taken to be a sequence of independent and identically distributed (i.i.d.) Gaussian random vectors uk ∈ N(0,I). The algorithm for identifying the nonlinear part is designed with multi-variable kernel functions. Under suitable conditions, we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one.
Keywords :
Gaussian processes; MIMO systems; approximation theory; convergence of numerical methods; linear systems; nonlinear functions; random processes; recursive estimation; set theory; vectors; Gaussian random vectors; MIMO Wiener systems; SA algorithm; independent and identically distributed Gaussian random vectors; linear subsystem; multiinput and multioutput Wiener system; multivariable kernel functions; nonlinear function convergence; probability; recursive identification; stochastic approximation algorithm; Approximation algorithms; Approximation methods; Convergence; Estimation; Kernel; MIMO; Vectors; $alpha$ -mixing; MIMO Wiener system; stochastic approximation; strong consistency;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2012.2215539
