timsac (version 1.3.0)

optsim: 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 $m$ columns of transition matrix, where $m$ 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)