Discrete ZNN models of Adams-Bashforth (AB) type solving various future problems with motion control of mobile manipulator

Inverse-Free DZNN Models for Solving Time-Dependent Linear System via High-Precision Linear Six-Step Method

Time-dependent linear system (TDLS) is usually encountered in scientific research, which is the mathematical formulation of many practical applications. Different from conventional inverse-need models, by utilizing zeroing neural network (ZNN) method twice, an inverse-free continuous ZNN (CZNN) model is developed for solving TDLS. For conveniently practical use, a discrete model is naturally desired. Superior to conventional discretization methods, a general linear six-step (LSS) method with the seventh-order precision and five variable parameters is proposed for the first time. Constraints about five variable parameters are theoretically analyzed to guarantee the efficacy of the general LSS method. Within constraints, 12 specific LSS methods are further developed. Aided with the general LSS method, an inverse-free discrete ZNN (DZNN) is proposed and termed DZNN-LSS model, and its precision is greatly improved compared with conventional discrete models. For comparison, three conventional discretization methods are also utilized to generate DZNN models. Detailed theoretical analyses are provided to prove the efficacy of relevant models. In addition, a specific TDLS example is considered to show the effectiveness and superiority of the DZNN-LSS model. More than that, applications to manipulator control and sound source localization are conducted to illustrate the applicability of the DZNN-LSS model.

Novel adaptive zeroing neural dynamics schemes for temporally-varying linear equation handling applied to arm path following and target motion positioning

While the handling for temporally-varying linear equation (TVLE) has received extensive attention, most methods focused on trading off the conflict between computational precision and convergence rate. Different from previous studies, this paper proposes two complete adaptive zeroing neural dynamics (ZND) schemes, including a novel adaptive continuous ZND (ACZND) model, two general variable time discretization techniques, and two resultant adaptive discrete ZND (ADZND) algorithms, to essentially eliminate the conflict. Specifically, an error-related varying-parameter ACZND model with global and exponential convergence is first designed and proposed. To further adapt to the digital hardware, two novel variable time discretization techniques are proposed to discretize the ACZND model into two ADZND algorithms. The convergence properties with respect to the convergence rate and precision of ADZND algorithms are proved via rigorous mathematical analyses. By comparing with the traditional discrete ZND (TDZND) algorithms, the superiority of ADZND algorithms in convergence rate and computational precision is shown theoretically and experimentally. Finally, simulative experiments, including numerical experiments on a specific TVLE solving as well as four application experiments on arm path following and target motion positioning are successfully conducted to substantiate the efficacy, superiority, and practicability of ADZND algorithms.

Stabilization for a class of delay systems via Z-type control

This paper investigates the Z-type control method to stabilize species populations and make them converge to desired values in a two-species predator-prey model with time delay in the prey species' growth rate. Direct controllers that assume both species' growth rates can be altered through human intervention and indirect controllers that assume only one species' growth can be changed at will are constructed. The Z-type method of construction is theoretically justified, and the potential for certain non-linear activation functions to speed up the control process is highlighted. A general procedure for discretizing state-space systems using the Euler forward formula is described. The discrete versions of the directly and indirectly controlled systems are provided. All Z-type controllers constructed are validated through numerical simulations.

Explicit Linear Left-and-Right 5-Step Formulas With Zeroing Neural Network for Time-Varying Applications

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.