Zeroing Neural Network for Real-Time Operational Research and Computational Intelligence: An Ordinary Differential Equation Based Approach

The zeroing neural network (ZNN), a canonical recurrent neural network, was developed in previous studies to address time-varying problem-solving scenarios. Numerous practical applications involve time-varying linear equations and inequality systems that demand real-time solutions. This article proposes a ZNN model specifically designed to solve such time-varying linear systems. Innovatively, it incorporates a new non-negative slack variable that transforms complex time-varying inequality systems into more easily solvable time-varying equation systems. By using an exponential decay formula and establishing an indefinite error function, the ZNN model is built. The suggested ZNN model's convergence properties are validated by theoretical research. Results from comparative simulations further support the superiority and effectiveness of the ZNN model in resolving inequality systems and time-varying linear equations.