@article {SIMOS2022,
	title = {Finite-time convergent zeroing neural network for solving time-varying algebraic Riccati equations},
	journal = {Journal of the Franklin Institute},
	year = {2022},
	abstract = {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.},
	issn = {0016-0032},
	doi = {https://doi.org/10.1016/j.jfranklin.2022.05.021},
	url = {https://www.sciencedirect.com/science/article/pii/S001600322200309X},
	author = {Theodore E. Simos and Vasilios N. Katsikis and Spyridon D. Mourtas and Predrag S. Stanimirovi{\'c}}
}
