Novel Discretized Zeroing Neural Network Models for Time-Varying Optimization Aided With Predictor-Corrector Methods

Abstract

In this article, we derive the predictor-corrector (PC) methods with three-order convergent precision, together with a class of specific general linear three-step (GLTS) rules provided. Afterward, a time-varying optimization (TVO) problem, which is deemed as a discrete TVO has been formulated and studied. The classical discrete zeroing neural network via Zhang et al. discretization (ZD-DZNN) is often utilized to obtain the solution. Actually, the stepsize domain of the DZNN model is a great factor for the dynamical stability. To enlarge the stepsize domain of the DZNN model, specific GLTS-type PC-DZNN models are applied to solve the TVO problem. Theoretical analyses show that better stability of the DZNN can be achieved by PC methods. Numerical simulative comparisons between the proposed PC-DZNN models and the ZD-DZNN in terms of stability are provided for further illustrations. In addition, motion planning of a PA10 manipulator and physical kinematics on UR5 formed as a TVO problem has been solved efficiently by applying the specific GLTS-type PC-DZNN models.