simcon {timsac} | R Documentation |
Produce optimal controller gain and simulate the controlled process.
simcon(span, len, r, arcoef, impulse, v, weight)
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. |
impulse |
impulse response matrices. |
v |
covariance matrix of innovation. |
weight |
weighting matrix of performance. |
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) - ... - A(p)y(t-p) = u(t) - B(1)u(t-1) - ... - B(p-1)u(t-p+1),
where A(i) (i=1,...,p) are the autoregressive coefficients of the ARMA representation of y(t).
gain |
controller gain. |
ave |
average value of i-th component of |
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. |
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.
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)