optdes {timsac} | R Documentation |
Compute optimal controller gain matrix for a quadratic criterion defined by two positive definite matrices Q and R.
optdes(y, max.order = NULL, ns, q, r)
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
|
ns |
number of D.P. stages. |
q |
positive definite (m, m) matrix Q, where m is the number of controlled variables. A quadratic criterion is defined by Q and R. |
r |
positive definite (l, l) matrix R, where l is the number of manipulated variables. |
perr |
prediction error covariance matrix. |
trans |
first m columns of transition matrix, where m is the number of controlled variables. |
gamma |
gamma matrix. |
gain |
gain matrix. |
H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.
# 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) optdes(y, ns = 20, q = q.mat, r = r.mat)