Premium
Optimal control of second‐order and high‐order descriptor systems
Author(s) -
Zhang Liping,
Zhang Guoshan,
Liu Wanquan
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2511
Subject(s) - riccati equation , algebraic riccati equation , mathematics , matrix (chemical analysis) , optimal control , linearization , matrix difference equation , singular value decomposition , transformation (genetics) , order (exchange) , control theory (sociology) , transformation matrix , linear quadratic gaussian control , nonlinear system , mathematical optimization , control (management) , computer science , mathematical analysis , partial differential equation , algorithm , materials science , artificial intelligence , chemistry , composite material , biochemistry , kinematics , classical mechanics , quantum mechanics , physics , finance , economics , gene
Summary This study investigates the optimal control problem of second‐order descriptor systems. The optimal control is characterized by using a new second‐order generalized Riccati equation, which is directly derived in terms of the original coefficient matrices of the system. Under some assumption conditions, applying matrix's singular value decomposition and matrix transformation, a nonlinear generalized Riccati matrix equation is transformed into a linear matrix equation, and the optimal control gain can be determined by solving the linear matrix equation. Furthermore, relevant results are also extended to the optimal control problems for the high‐order descriptor system. Finally, several simulation examples and the comparison with the existing linearization method are provided to illustrate the effectiveness of the developed approach.