In this paper, a neurodynamic algorithm with finite-time convergence to solve $${L_{\mathrm{{1}}}}$$ -minimization problem is proposed for sparse signal reconstruction which is based on projection neural network (PNN). Compared with the existing PNN, the proposed algorithm is combined with the sliding mode technique in control theory. Under certain conditions, the stability of the proposed algorithm in the sense of Lyapunov is analyzed and discussed, and then the finite-time convergence of the proposed algorithm is proved and the setting time bound is given. Finally, simulation results on a numerical example and a contrast experiment show the effectiveness and superiority of our proposed neurodynamic algorithm.

中文翻译：

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一种有限时间收敛稀疏信号重建的神经动力学算法

在本文中，提出了一种具有有限时间收敛性的神经动力学算法来解决$${L_{\mathrm{{1}}}}$$ -最小化问题，用于基于投影神经网络（PNN）的稀疏信号重建。与现有的PNN相比，该算法结合了控制理论中的滑模技术。在一定条件下，分析讨论了该算法在Lyapunov意义下的稳定性，然后证明了该算法的有限时间收敛性，并给出了设定时间界。最后，数值例子和对比实验的模拟结果表明了我们提出的神经动力学算法的有效性和优越性。