optdes {timsac}R Documentation

Optimal Controller Design

Description

Computr 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 (ir, ir) matrix Q, where ir is the number of controlled variables.
A quadratic criterion is defined by Q and R.
r positive definite (il, il) matrix R, where il is th number of maninpulated variables.

Value

perr prediction error covariance matrix.
trans first ir columns of transition matrix, where ir 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)

[Package timsac version 1.2.1 Index]