Research Article
Optimal Control for a Linear System Subject to a General ARIMA Disturbance
Table 2
AMSE when the initial bias’ mean and standard deviation vary.
is the ARIMA(1, 1, 1) disturbance with
and
.
| ARIMA controller | | | 1 | 2 | 3 | 4 |
| −4 | 1.176 (.006) | 1.180 (.007) | 1.203 (.008) | 1.244 (.010) | 1.304 (.013) | −3 | 1.106 (.006) | 1.110 (.006) | 1.134 (.007) | 1.176 (.009) | 1.237 (.011) | −2 | 1.055 (.005) | 1.061 (.005) | 1.085 (.006) | 1.128 (.008) | 1.190 (.010) | −1 | 1.025 (.005) | 1.031 (.005) | 1.057 (.005) | 1.101 (.007) | 1.163 (.009) | 0 | 1.014 (.005) | 1.021 (.005) | 1.048 (.005) | 1.093 (.006) | 1.156 (.008) | 1 | 1.024 (.005) | 1.032 (.005) | 1.059 (.005) | 1.105 (.007) | 1.169 (.009) | 2 | 1.053 (.005) | 1.062 (.005) | 1.091 (.006) | 1.137 (.008) | 1.202 (.010) | 3 | 1.103 (.006) | 1.113 (.006) | 1.142 (.007) | 1.189 (.009) | 1.255 (.011) | 4 | 1.172 (.007) | 1.183 (.007) | 1.213 (.008) | 1.261 (.011) | 1.328 (.013) |
| controller | | | 1 | 2 | 3 | 4 |
| −4 | 1.279 (.007) | 1.284 (.008) | 1.311 (.010) | 1.360 (.012) | 1.432 (.016) | −3 | 1.194 (.006) | 1.200 (.007) | 1.228 (.008) | 1.279 (.010) | 1.351 (.013) | −2 | 1.133 (.006) | 1.140 (.006) | 1.170 (.007) | 1.221 (.009) | 1.294 (.011) | −1 | 1.096 (.005) | 1.105 (.005) | 1.135 (.006) | 1.187 (.008) | 1.261 (.010) | 0 | 1.084 (.005) | 1.093 (.005) | 1.124 (.006) | 1.177 (.007) | 1.253 (.010) | 1 | 1.095 (.005) | 1.105 (.005) | 1.137 (.006) | 1.192 (.008) | 1.268 (.010) | 2 | 1.130 (.006) | 1.141 (.006) | 1.174 (.007) | 1.230 (.009) | 1.307 (.011) | 3 | 1.189 (.007) | 1.201 (.007) | 1.235 (.008) | 1.292 (.010) | 1.370 (.013) | 4 | 1.272 (.007) | 1.285 (.008) | 1.320 (.009) | 1.378 (.012) | 1.458 (.016) |
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The corresponding SEAMSE’s are enclosed in the parentheses. Neither measurement errors nor adjustment errors are considered in the simulations.
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