Abstract
In this article, time-varying matrix equation problems, including the Lyapunov equation, matrix inversion, and generalized matrix inversion are investigated in a future (or say, discrete time-varying) perspective. Then, in order to develop a unified solution model for the above three future problems, a future matrix equation (FME) is investigated. The discrete-time unified solution (DTUS) model, which is based on the zeroing neural dynamics (ZND) method and a new nine-instant Zhang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> discretization (ZeaD) formula, is thus proposed and termed the nine-instant DTUS (9IDTUS) model. Meanwhile, theoretical analyses on the stability and precision of the 9IDTUS model are provided. In addition, conventional DTUS models obtained from the Euler forward formula, Taylor–Zhang discretization formula, and a seven-instant discretization formula are also presented for comparisons. Furthermore, numerical experiments including the robot motion generation, are conducted and analyzed to substantiate the efficacy and superiority of the proposed 9IDTUS model.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IEEE Transactions on Systems, Man, and Cybernetics: Systems
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
