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)

The corresponding SEAMSE’s are enclosed in the parentheses. Neither measurement errors nor adjustment errors are considered in the simulations.