timsac (version 1.3.8)

optdes: 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)

Value

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.

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 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.

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)