Two types of anti-noise integral enhanced recurrent neural networks for solving time-varying complex quadratic programming

Abstract

The time-varying complex quadratic programming problem plays an important role in scientific research and engineering applications, and has received extensive attention. In this paper, by solving the problem in different number domains, two types of novel anti-noise integral enhanced recurrent neural networks (IERNNs) are proposed and analyzed. Specifically, the IERNN-A model solves the problems in the complex number domain, while the IERNN-B model solves the problems by converting the problems from the complex number domain into the real number domain. Both the IERNN-A and IERNN-B have the same design paradigm, i.e., an integral-type error function is first defined to obtain good anti-noise capability, and then substitute it into a differential-driven design formula to ensure convergence. Theory analysis and simulation results verify the global convergence and robustness of the proposed IERNNs. Furthermore, if a linear activation is used, the exponential convergence rate is obtained. Meanwhile, when time-varying bounded noise exists, the IERNNs are input-to-state stable. In addition, compared with other art-of-the-state methods, the proposed methods have faster convergence speed, stronger noise-suppression ability, and no overshoot, which are verified by the simulation and application of manipulator trajectory tracking.