optsim: Optimal Control Simulation

In timsac: Time Series Analysis and Control Package

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), nrow = 3, ncol = 3, byrow = TRUE)
ar[, , 2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3), nrow = 3, ncol = 3, byrow = TRUE)
x <- matrix(rnorm(200*3), nrow = 200, ncol = 3)
y <- mfilter(x, ar, "recursive")
q.mat <- matrix(c(0.16,0,0,0.09), nrow = 2, ncol = 2)
r.mat <- as.matrix(0.001)
optsim(y, max.order = 10, ns = 20, q = q.mat, r = r.mat, len = 20)

timsac documentation built on Sept. 30, 2023, 5:06 p.m.