A Discrete Sliding-Mode Reaching-Law Zeroing Neural Solution for Dynamic Constrained Quadratic Programming

Various discrete-time zeroing neural network (DTZNN) models have been developed for solving dynamic constrained quadratic programming. However, two challenges persist within the DTZNN framework: first, the theoretical analysis of robustness in disturbance suppression remains insufficient; second, to the best of authors' knowledge, existing DTZNN models have yet to provide a theoretical proof of finite-step convergence. Inspired by the inherent robustness and finite-step convergence of discrete sliding-mode control based on the reaching-law, this article is the first work to integrate reaching-law theory into the DTZNN framework to address the aforementioned challenges, ensuring that the resulting DTZNN exhibits both robustness and finite-step convergence. In addition, a novel hyperbolic type reaching law (HTRL) is designed, which offers advantages in reducing the width of the quasi-sliding-mode region and suppressing chattering. The zeroing neural network (ZNN) based on this HTRL (HTRL-ZNN) is rigorously proven to exhibit effective disturbance suppression robustness and finite-step convergence, with an explicit expression provided for the convergence step length. Finally, the effectiveness and advantages of HTRL-ZNN in solving dynamic constrained quadratic programming are validated through both a numerical example and an application-oriented case.