optdes {timsac}R Documentation

Optimal Controller Design

Description

Compute optimal controller gain matrix for a quadratic criterion defined by two positive definite matrices Q and R.

Usage

  optdes(y, max.order = NULL, ns, q, r)

Arguments

y

a multivariate time series.

max.order

upper limit of model order. Default is 2n2 \sqrt{n}, where nn is the length of the time series y.

ns

number of D.P. stages.

q

positive definite (m,m)(m, m) matrix QQ, where mm is the number of controlled variables. A quadratic criterion is defined by QQ and RR.

r

positive definite (l,l)(l, l) matrix RR, where ll is the number of manipulated variables.

Value

perr

prediction error covariance matrix.

trans

first mm columns of transition matrix, where mm is the number of controlled variables.

gamma

gamma matrix.

gain

gain matrix.

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)
optdes(y, ns = 20, q = q.mat, r = r.mat)

[Package timsac version 1.3.8-4 Index]