Zeroing neural network with comprehensive performance and its applications to time-varying Lyapunov equation and perturbed robotic tracking

Abstract

The time-varying Lyapunov equation is an important problem that has been extensively employed in the engineering field and the Zeroing Neural Network (ZNN) is a powerful tool for solving such problem. However, unpredictable noises can potentially harm ZNN’s accuracy in practical situations. Thus, the comprehensive performance of the ZNN model requires both fast convergence rate and strong robustness, which are not easy to accomplish. In this paper, based on a new neural dynamic, a novel Noise-Tolerance Finite-time convergent ZNN (NTFZNN) model for solving the time-varying Lyapunov equations has been proposed. The NTFZNN model simultaneously converges in finite time and have stable residual error even under unbounded time-varying noises. Furthermore, the Simplified Finite-te convergent Activation Function (SFAF) with simpler structure is used in the NTFZNN model to reduce model complexity while retaining finite convergence time. Theoretical proofs and numerical simulations are provided in this paper to substantiate the NTFZNN model’s convergence and robustness performances, which are better than performances of the ordinary ZNN model and the Noise-Tolerance ZNN (NTZNN) model. Finally, simulation experiment of using the NTFZNN model to control a wheeled robot manipulator under perturbation validates the superior applicability of the NTFZNN model.