timsac (version 1.3.8)

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)

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 \(Y^2\).

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.

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)