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| -rw-r--r-- | R/rarx.R | 44 | ||||
| -rw-r--r-- | man/rarx.Rd | 55 |
2 files changed, 98 insertions, 1 deletions
@@ -1,3 +1,45 @@ +#' Estimate parameters of ARX recursively +#' +#' Estimates the parameters of a single-output ARX model of the +#' specified order from data using the recursive weighted least-squares +#' algorithm. +#' +#' @param x an object of class \code{idframe} +#' @param order Specification of the orders: the three integer components +#' (na,nb,nk) are the order of polynolnomial A, (order of polynomial B + 1) and +#' the input-output delay +#' @param lambda Forgetting factor(Default=\code{0.95}) +#' +#' @return +#' A list containing the following objects +#' \describe{ +#' \item{theta}{Estimated parameters of the model. The \eqn{k^{th}} +#' row contains the parameters associated with the \eqn{k^{th}} +#' sample. Each row in \code{theta} has the following format: \cr +#' theta[i,:]=[a1,a2,...,ana,b1,...bnb] +#' } +#' \item{yhat}{Predicted value of the output, according to the +#' current model - parameters based on all past data} +#' } +#' +#' @references +#' Arun K. Tangirala (2015), \emph{Principles of System Identification: +#' Theory and Practice}, CRC Press, Boca Raton. Section 25.1.3 +#' +#' Lennart Ljung (1999), \emph{System Identification: Theory for the User}, +#' 2nd Edition, Prentice Hall, New York. Section 11.2 +#' @examples +#' Gp1 <- idpoly(c(1,-0.9,0.2),2,ioDelay=2,noiseVar = 0.1) +#' Gp2 <- idpoly(c(1,-1.2,0.35),2.5,ioDelay=2,noiseVar = 0.1) +#' uk = idinput(2044,'prbs',c(0,1/4)); N = length(uk); +#' N1 = round(0.35*N); N2 = round(0.4*N); N3 = N-N1-N2; +#' yk1 <- sim(Gp1,uk[1:N1],addNoise = T) +#' yk2 <- sim(Gp2,uk[N1+1:N2],addNoise = T) +#' yk3 <- sim(Gp1,uk[N1+N2+1:N3],addNoise = T) +#' yk <- c(yk1,yk2,yk3) +#' z <- idframe(yk,uk,1) +#' g(theta,yhat) %=% rarx(z,c(2,1,2)) +#' #' @export rarx <- function(x,order=c(1,1,1),lambda=0.95){ y <- outputData(x); u <- inputData(x) @@ -33,5 +75,5 @@ rarx <- function(x,order=c(1,1,1),lambda=0.95){ theta[i+1,] <- t(t(theta[i,,drop=F])+eps_i[1]*kappa_i) Plast <- (diag(na+nb)-kappa_i%*%t(temp))%*%Plast/lambda } - list(theta=theta,yhat=yhat,P=Plast) + list(theta=theta,yhat=yhat) }
\ No newline at end of file diff --git a/man/rarx.Rd b/man/rarx.Rd new file mode 100644 index 0000000..5e067dd --- /dev/null +++ b/man/rarx.Rd @@ -0,0 +1,55 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/rarx.R +\name{rarx} +\alias{rarx} +\title{Estimate parameters of ARX recursively} +\usage{ +rarx(x, order = c(1, 1, 1), lambda = 0.95) +} +\arguments{ +\item{x}{an object of class \code{idframe}} + +\item{order}{Specification of the orders: the three integer components +(na,nb,nk) are the order of polynolnomial A, (order of polynomial B + 1) and +the input-output delay} + +\item{lambda}{Forgetting factor(Default=\code{0.95})} +} +\value{ +A list containing the following objects +\describe{ + \item{theta}{Estimated parameters of the model. The \eqn{k^{th}} + row contains the parameters associated with the \eqn{k^{th}} + sample. Each row in \code{theta} has the following format: \cr + theta[i,:]=[a1,a2,...,ana,b1,...bnb] + } + \item{yhat}{Predicted value of the output, according to the + current model - parameters based on all past data} +} +} +\description{ +Estimates the parameters of a single-output ARX model of the +specified order from data using the recursive weighted least-squares +algorithm. +} +\examples{ +Gp1 <- idpoly(c(1,-0.9,0.2),2,ioDelay=2,noiseVar = 0.1) +Gp2 <- idpoly(c(1,-1.2,0.35),2.5,ioDelay=2,noiseVar = 0.1) +uk = idinput(2044,'prbs',c(0,1/4)); N = length(uk); +N1 = round(0.35*N); N2 = round(0.4*N); N3 = N-N1-N2; +yk1 <- sim(Gp1,uk[1:N1],addNoise = T) +yk2 <- sim(Gp2,uk[N1+1:N2],addNoise = T) +yk3 <- sim(Gp1,uk[N1+N2+1:N3],addNoise = T) +yk <- c(yk1,yk2,yk3) +z <- idframe(yk,uk,1) +g(theta,yhat) \%=\% rarx(z,c(2,1,2)) + +} +\references{ +Arun K. Tangirala (2015), \emph{Principles of System Identification: +Theory and Practice}, CRC Press, Boca Raton. Section 25.1.3 + +Lennart Ljung (1999), \emph{System Identification: Theory for the User}, +2nd Edition, Prentice Hall, New York. Section 11.2 +} + |