A fixed-time convergent and noise-tolerant zeroing neural network for online solution of time-varying matrix inversion

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As a common mathematical operation, the time-varying matrix inversion (TVMI) is frequently arisen in many complex problems. It has been proved in a large number of studies that the zeroing neural network (ZNN) is a reliable tool to solve TVMI problems. However, the previous reported conventional zeroing neural network (CZNN) models only achieve undesirable exponential convergence or finite-time convergence, and they are difficult to be popularized in practical applications. Therefore, by introducing a novel activation function (NAF), a fixed-time convergence and noise-tolerant zeroing neural network (FTCNTZNN) model for solving TVMI problems is proposed in this paper. Different from existing CZNN models, the proposed FTCNTZNN model possesses both fixed-time convergence and anti-noise properties for TVMI solving. To comprehensively show the superiority of the proposed FTCNTZNN model for solving TVMI, a lot of theoretical demonstrations and comparative simulation experiments have been provided in this work. Firstly, the fixed-time convergence and robustness of the proposed FTCNTZNN model are verified by detailed theoretical analysis in noiseless and noisy environment, respectively. Then, the proposed FTCNTZNN model is applied to solve two different TVMI problems in a variety of situations. In addition, a successful manipulator trajectory tracking application using the proposed FTCNTZNN model in noisy environment further validates its practicability. Both of theoretical analysis and experimental results convincingly verify that the proposed FTCNTZNN model can effectively solve TVMI problems in noiseless and noisy environment.