timsac (version 1.3.0)

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)

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.

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.

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),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(200*3),200,3)
  y <- mfilter(x,ar,"recursive")
  q <- matrix(c(0.16,0,0,0.09), 2, 2)
  r <- matrix(0.001, 1, 1)
  optdes(y,, ns=20, q, r)