optsim {timsac}R Documentation

Optimal Control Simulation

Description

Perform optimal control simulation and evaluate the means and variances of the controlled and manipulated variables X and Y.

Usage

  optsim(y, max.order=NULL, ns, q, r, noise=NULL, len, plot=TRUE)

Arguments

y a multivariate time series.
max.order upper limit of model order. Default is 2*sqrt(n), where n is the length of the time series y.
ns number of steps of simulation.
q positive definite matrix Q.
r positive definite matrix R.
noise noise. If not provided, Gaussian vector white noise with the length len is generated.
len length of white noise record.
plot logical. If TRUE (default) controlled variables X and manipulated variables Y are plotted.

Value

trans first ir columns of transition matrix, where ir is the number of controlled variables.
gamma gamma matrix.
gain gain matrix.
convar controlled variables X.
manvar manipulated variables Y.
xmean mean of X.
ymean mean of Y.
xvar variance of X.
yvar variance of Y.
x2sum sum of X^2.
y2sum sum of Y^2.
x2mean mean of X^2.
y2mean mean of Y^2.

References

H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.

Examples

# Multivariate Example Data
  ar <- array(0,dim=c(3,3,2))
  ar[,,1] <- matrix(c(0.4,  0,   0.3,
                      0.2, -0.1, -0.5,
                      0.3,  0.1, 0),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(200*3),200,3)
  y <- mfilter(x,ar,"recursive")
  q <- matrix(c(0.16,0,0,0.09), 2, 2)
  r <- matrix(0.001, 1, 1)
  optsim(y, max.order=10, ns=20, q, r, len=20)

[Package timsac version 1.2.1 Index]