R: Optimal Controller Design

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 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)

[Package timsac version 1.3.5 Index]