simcon: Optimal Controller Design and Simulation

In timsac: Time Series Analysis and Control Package

Optimal Controller Design and Simulation

Description

Produce optimal controller gain and simulate the controlled process.

Usage

simcon(span, len, r, arcoef, impulse, v, weight)

Arguments

span	span of control performance evaluation.
len	length of experimental observation.
r	dimension of control input, less than or equal to d (dimension of a vector).
arcoef	matrices of autoregressive coefficients. arcoef[i,j,k] shows the value of i-th row, j-th column, k-th order.
impulse	impulse response matrices.
v	covariance matrix of innovation.
weight	weighting matrix of performance.

Details

The basic state space model is obtained from the autoregressive moving average model of a vector process y(t);

y(t) - A(1)y(t-1) -\ldots- A(p)y(t-p) = u(t) - B(1)u(t-1) -\ldots- B(p-1)u(t-p+1),

where A(i) (i=1,\ldots,p) are the autoregressive coefficients of the ARMA representation of y(t).

Value

gain	controller gain.
ave	average value of i-th component of y.
var	variance.
std	standard deviation.
bc	sub matrices (pd,r) of impulse response matrices, where p is the order of the process, d is the dimension of the vector and r is the dimension of the control input.
bd	sub matrices (pd,d-r) of impulse response matrices.

References

H.Akaike, E.Arahata and T.Ozaki (1975) Computer Science Monograph, No.6, Timsac74, A Time Series Analysis and Control Program Package (2). The Institute of Statistical Mathematics.

Examples

x <- matrix(rnorm(1000*2), nrow = 1000, ncol = 2)
ma <- array(0, dim = c(2,2,2))
ma[, , 1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), nrow = 2, ncol = 2, byrow = TRUE)
ma[, , 2] <- matrix(c( -0.2,  0.0,
                       -0.1, -0.3), nrow = 2, ncol = 2, byrow = TRUE)
y <- mfilter(x, ma, "convolution")

ar <- array(0, dim = c(2,2,3))
ar[, , 1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), nrow = 2, ncol = 2, byrow = TRUE)
ar[, , 2] <- matrix(c( -0.5, -0.2,
                       -0.2, -0.5), nrow = 2, ncol = 2, byrow = TRUE)
ar[, , 3] <- matrix(c( -0.3, -0.05,
                       -0.1, -0.3), nrow = 2, ncol = 2, byrow = TRUE)
y <- mfilter(y, ar, "recursive")

z <- markov(y)
weight <-  matrix(c(0.0002,  0.0,
                    0.0,     2.9 ), nrow = 2, ncol = 2, byrow = TRUE)
simcon(span = 50, len = 700, r = 1, z$arcoef, z$impulse, z$v, weight)

timsac documentation built on Sept. 30, 2023, 5:06 p.m.