R: Optimal Control Simulation

optsim {timsac} | R Documentation

## Optimal Control Simulation

### Description

Perform optimal control simulation and evaluate the means and variances of the controlled and manipulated variables X and Y.

### Usage

      optsim(y, max.order = NULL, ns, q, r, noise = NULL, len, plot = TRUE)

### 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 steps of simulation.
`q` | positive definite matrix Q.
`r` | positive definite matrix R.
`noise` | noise. If not provided, Gaussian vector white noise with the length `len` is generated.
`len` | length of white noise record.
`plot` | logical. If `TRUE` (default), controlled variables X and manipulated variables Y are plotted.

### Value

`trans` | first m columns of transition matrix, where m is the number of controlled variables.
`gamma` | gamma matrix.
`gain` | gain matrix.
`convar` | controlled variables X.
`manvar` | manipulated variables Y.
`xmean` | mean of X.
`ymean` | mean of Y.
`xvar` | variance of X.
`yvar` | variance of Y.
`x2sum` | sum of X^2.
`y2sum` | sum of Y^2.
`x2mean` | mean of X^2.
`y2mean` | mean of Y^2.

### 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)
    optsim(y, max.order = 10, ns = 20, q = q.mat, r = r.mat, len = 20)

[Package timsac version 1.3.6 Index]