Noise-suppressing zeroing neural network for online solving time-varying matrix square roots problems: A control-theoretic approach

In this paper, the noise-suppressing zeroing neural network models (NSZNNMs) for online solving time-varying matrix square roots problems (TVMSRPs) are revisited and redesigned from a control viewpoint framework. Specifically, to solve TVMSRPs with different noises in real time, some noise-suppressing zeroing neural network functions are proposed. Moreover, a novel generally noise-suppressing zeroing neural network model (GNSZNNM) with generally noise-suppressing time-varying error-monitoring function is developed for online solving TVMSRPs with different measurement noises. In particular, the developed NSZNNMs globally converge to the time-varying theoretical solution of the TVMSRPs without noises, and exponentially converge to the theoretical solutions in the presence of noises, which are verified and analyzed theoretically. Compared with the classical zeroing neural network model (ZNNM), numerical results are provided to substantiate the efficiency and superiority of the developed NSZNNMs for online solving TVMSRPs with inherent tolerance to noises. In addition, a time-varying tensor square root problem is provided and illustrated to substantiate the potentially practical applications of the proposed NSZNNM for real-time TVMSRPs. The obtained results indicate that different activation functions can be utilized to accelerate the convergence speed of the GNSZNNM, which demonstrates its high efficiency and robustness.