TY - GEN
T1 - Performance Degradation of an Optimal LQ Controller based on a Reduced-Order Observer Designed via the Sylvester Algebraic Equation
AU - Radisavljevic-Gajic, Verica
AU - Safieh, Faris Omar Mohmoud
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025
Y1 - 2025
N2 - This paper considers the problem of an optimal linear-quadratic (LQ) control based on a reduced-order observer (ROO) designed via the Sylvester equation. Since observers estimate state variables with certain errors, the optimal performance gets degraded in the case when observer estimates are used for feedback instead of the system states. In this work, the analytical expression is derived for the optimal LQ criterion loss for steady state optimization. The paper derives a formula based on the least square method for the selection of initial conditions of ROO that can drastically reduce the optimal performance loss. Since in some applications of ROO with LQ optimal controllers the performance loss can be very high it is mandatory that the corresponding applications be reexamined in the spirit of the results reported in this paper.
AB - This paper considers the problem of an optimal linear-quadratic (LQ) control based on a reduced-order observer (ROO) designed via the Sylvester equation. Since observers estimate state variables with certain errors, the optimal performance gets degraded in the case when observer estimates are used for feedback instead of the system states. In this work, the analytical expression is derived for the optimal LQ criterion loss for steady state optimization. The paper derives a formula based on the least square method for the selection of initial conditions of ROO that can drastically reduce the optimal performance loss. Since in some applications of ROO with LQ optimal controllers the performance loss can be very high it is mandatory that the corresponding applications be reexamined in the spirit of the results reported in this paper.
KW - Reduced-order observer (ROO)
KW - Sylvester equation design
KW - linear-quadratic optimal performance loss
UR - https://www.scopus.com/pages/publications/105035721817
U2 - 10.1109/ICECER65523.2025.11401179
DO - 10.1109/ICECER65523.2025.11401179
M3 - Conference contribution
AN - SCOPUS:105035721817
T3 - International Conference on Electrical and Computer Engineering Researches, ICECER 2025
BT - International Conference on Electrical and Computer Engineering Researches, ICECER 2025
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2025 International Conference on Electrical and Computer Engineering Researches, ICECER 2025
Y2 - 6 December 2025 through 8 December 2025
ER -