Noise-tolerant neural algorithm for online solving Yang-Baxter-type matrix equation in the presence of noises: A control-based method

• Published in: Neurocomputing (Amsterdam) Vol. 424; pp. 84 - 96
• Main Authors: Shi, Tian, Tian, Yantao, Sun, Zhongbo, Liu, Keping, Jin, Long, Yu, Junzhi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2021
• Subjects: Convergence performance; Noise-tolerant neural algorithm; Online solution; Time-varying matrix problem; Yang-Baxter-type matrix equation; Online solution; Yang-Baxter-type matrix equation; Convergence performance; Noise-tolerant neural algorithm; Time-varying matrix problem
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2020.10.110

•The NTZNNM is developed for the solution of time-invariant/varying Yang-Baxter-type matrix equation problem in the presence of noises from a control-theoretic viewpoint.•The time-varying matrix-formed state variable of NTZNNM is proven to globally/exponentially converge to the matrix-formed theoretical solution.•The robustness and superiority of GNTZNNM are guaranteed with the aid of different activation functions for handling time-invariant/varying Yang-Baxter-type matrix equation problems. Time-invariant/varying Yang-Baxter-type matrix equation problems in the presence of noises often arise in the fields of scientific computation and engineering implementation. Noises are ubiquitous and unavoidable in real systems but most existing models carry out the time-invariant/varying Yang-Baxter-type matrix equation problem with an indispensable precondition that the solving process is free of noises. In this paper, a noise-tolerant zeroing neural network model (NTZNNM) is first proposed, analyzed and verified by feat of a classical zeroing neural network model (ZNNM) from a control-theoretic viewpoint, and note that NTZNNM behaves efficiently in online solving the time-invariant/varying Yang-Baxter-type matrix equation problem with different measurement noises. Moreover, a general noise-tolerant zeroing neural network model (GNTZNNM) derived from a general noise-tolerant zeroing neural dynamic model (GNTZNDM) is developed and utilized to accelerating the convergent rate and enhancing the robustness. Then, theoretical results further demonstrate that the presented NTZNNM owns the ability to globally/exponentially converge with different measurement noises. Furthermore, the global convergence of GNTZNDM with different monotonically-increasing odd activation functions is also investigated and analyzed in detail. Besides, numerical results are provided to substantiate the efficiency, availability and superiority of the developed NTZNNM and GNTZNNM for time-invariant/varying Yang-Baxter-type matrix equation problems with inherent tolerance to noises.