TY - JOUR
T1 - Convex Model-Based Reduced-Order Model for Uncertain Control Systems
AU - Yang, Chen
AU - Fan, Ziyao
AU - Xia, Yuanqing
N1 - Publisher Copyright:
IEEE
PY - 2024
Y1 - 2024
N2 - This study proposes a convex model-based reduced-order model (CMBROM) method for uncertain linear control systems, which ensures the accuracy of the reduced-order model with small samplings. Once the convex bounds of uncertainties are known, the coefficient matrices, input, and output in the uncertain state-space equation are quantified as convex model-based (CMB) parameters. A novel CMB state-space equation is constituted based on an order-extended matrix, which can solve the deterministic and uncertain parts of the state and output using the proposed solution method. The controllability and stability of the CMB state-space system have been proved. The conventional balance system is extended into a convex model format as an important fundamental process for order reduction, and the nominal and uncertain balanced coefficient matrices can be obtained using the transformation matrix. By solving the uncertain controllable and observability matrices using the CMB Lyapunov equation, a convex model perturbation-based singular value decomposition (SVD) is proposed to estimate the uncertain Hankel singular values. Finally, the CMB order-truncated criterion is set using the CMB possibility.
AB - This study proposes a convex model-based reduced-order model (CMBROM) method for uncertain linear control systems, which ensures the accuracy of the reduced-order model with small samplings. Once the convex bounds of uncertainties are known, the coefficient matrices, input, and output in the uncertain state-space equation are quantified as convex model-based (CMB) parameters. A novel CMB state-space equation is constituted based on an order-extended matrix, which can solve the deterministic and uncertain parts of the state and output using the proposed solution method. The controllability and stability of the CMB state-space system have been proved. The conventional balance system is extended into a convex model format as an important fundamental process for order reduction, and the nominal and uncertain balanced coefficient matrices can be obtained using the transformation matrix. By solving the uncertain controllable and observability matrices using the CMB Lyapunov equation, a convex model perturbation-based singular value decomposition (SVD) is proposed to estimate the uncertain Hankel singular values. Finally, the CMB order-truncated criterion is set using the CMB possibility.
KW - CMB order-truncated criterion
KW - CMB state-space equation
KW - Computational modeling
KW - Convex model-based (CMB) balance system
KW - Mathematical models
KW - Matrix decomposition
KW - Read only memory
KW - Symmetric matrices
KW - Uncertainty
KW - Vectors
KW - convex model perturbation-based singular value decomposition (SVD)
KW - optimization of order selection
UR - http://www.scopus.com/inward/record.url?scp=85190335997&partnerID=8YFLogxK
U2 - 10.1109/TSMC.2024.3373031
DO - 10.1109/TSMC.2024.3373031
M3 - Article
AN - SCOPUS:85190335997
SN - 2168-2216
SP - 1
EP - 11
JO - IEEE Transactions on Systems, Man, and Cybernetics: Systems
JF - IEEE Transactions on Systems, Man, and Cybernetics: Systems
ER -