<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Theodore E. Simos</style></author><author><style face="normal" font="default" size="100%">Vasilios N. Katsikis</style></author><author><style face="normal" font="default" size="100%">Spyridon D. Mourtas</style></author><author><style face="normal" font="default" size="100%">Predrag S. Stanimirović</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Finite-time convergent zeroing neural network for solving time-varying algebraic Riccati equations</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of the Franklin Institute</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.sciencedirect.com/science/article/pii/S001600322200309X</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Various forms of the algebraic Riccati equation (ARE) have been widely used to investigate the stability of nonlinear systems in the control field. In this paper, the time-varying ARE (TV-ARE) and linear time-varying (LTV) systems stabilization problems are investigated by employing the zeroing neural networks (ZNNs). In order to solve the TV-ARE problem, two models are developed, the ZNNTV-ARE model which follows the principles of the original ZNN method, and the FTZNNTV-ARE model which follows the finite-time ZNN (FTZNN) dynamical evolution. In addition, two hybrid ZNN models are proposed for the LTV systems stabilization, which combines the ZNNTV-ARE and FTZNNTV-ARE design rules. Note that instead of the infinite exponential convergence specific to the ZNNTV-ARE design, the structure of the proposed FTZNNTV-ARE dynamic is based on a new evolution formula which is able to converge to a theoretical solution in finite time. Furthermore, we are only interested in real symmetric solutions of TV-ARE, so the ZNNTV-ARE and FTZNNTV-ARE models are designed to produce such solutions. Numerical findings, one of which includes an application to LTV systems stabilization, confirm the effectiveness of the introduced dynamical evolutions.</style></abstract></record></records></xml>