Optimal control of second‐order and high‐order descriptor systems. (2nd May 2019)

• Record Type: Journal Article
• Authors: Zhang, Liping; Zhang, Guoshan; Liu, Wanquan
• Is Part Of: Optimal control applications and methods. Volume 40:Number 4(2019)
• Page Start: 791
• Page End: 806
• Publication Date: 2019-05-02
• Subjects: generalized Riccati equation -- optimal control -- second‐order singular system -- singular value decomposition; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2511
• Languages: English
• ISSNs: 0143-2087

Abstract

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.