Norm-Based Finite-Time Convergent Recurrent Neural Network for Dynamic Linear Inequality

Various recurrent neural network (RNN) models, especially zeroing neutral network (ZNN) models, have been investigated to solve time-varying linear inequalities (TVLI) and applied to different important fields. Existing ZNN models can solve TVLI in finite time by using complicated elementwise nonlinear functions, which brings a concern about cost for hardware implementation. To achieve a balance between implementation cost and convergence performance, this article explores a new RNN model based on ZNN by using a two-norm method for solving TVLI, which is called norm-based ZNN (NBZNN), and the proposed model can achieve finite-time convergence without the assistance of elementwise nonlinear activation functions. Strict theoretical analysis is given on convergence properties of the proposed model, showing its global finite-time convergence, which is preserved under a class of bounded noises. For the first time, our work shows that a finite-time convergent RNN model can be designed for solving TVLI without using elementwise nonlinear activation functions. Computer simulation results further verify the effectiveness and superiority of the proposed NBZNN model for solving TVLI. An application to robotics further demonstrates the efficacy of the proposed NBZNN model.