Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations

A novel discrete zeroing neural network for online solving time-varying nonlinear optimization problems

To reduce transportation time, a discrete zeroing neural network (DZNN) method is proposed to solve the shortest path planning problem with a single starting point and a single target point. The shortest path planning problem is reformulated as an optimization problem, and a discrete nonlinear function related to the energy function is established so that the lowest-energy state corresponds to the optimal path solution. Theoretical analyzes demonstrate that the discrete ZNN model (DZNNM) exhibits zero stability, effectiveness, and real-time performance in handling time-varying nonlinear optimization problems (TVNOPs). Simulations with various parameters confirm the efficiency and real-time performance of the developed DZNNM for TVNOPs, indicating its suitability and superiority for solving the shortest path planning problem in real time.

An advanced bionic knee joint mechanism with neural network controller

In this article, a tensegrity-based knee mechanism is studied for developing a high-efficiency rehabilitation knee exoskeleton. Moreover, the kinematics and dynamics models of the knee mechanism are explored for bringing about further improvement in controller design. In addition, to estimate the performance of the bionic knee joint, based on the limit function of knee patella, the limit position functionality of the bionic knee joint is developed for enhancing the bionic property. Furthermore, to eliminate the noise item and other disturbances that are constantly generated in the rehabilitation process, a noise-tolerant zeroing neural network (NTZNN) algorithm is utilized to establish the controller. This indicates that the controller shows an anti-noise performance; hence, it is quite unique from other bionic knee mechanism controllers. Eventually, the anti-noise performance and the calculation of the precision of the NTZNN controller are verified through several simulation and contrast results.

Unified Model Solving Nine Types of Time-Varying Problems in the Frame of Zeroing Neural Network

Many time-varying problems have been solved using the zeroing neural network proposed by Zhang et al. In this article, nine types of time-varying problems, namely time-varying nonlinear equation system, time-varying linear equation system, time-varying convex nonlinear optimization under linear equalities, unconstrained time-varying convex nonlinear optimization, time-varying convex quadratic programming under linear equalities, unconstrained time-varying convex quadratic programming, time-varying nonlinear inequality system, time-varying linear inequality system, and time-varying division, are investigated to better understand the essence of zeroing neutral network. Discrete-form time-varying problems are studied by considering the nature of unknown future and the requirement of real-time computation for time-varying problems. A unified model is proposed in the frame of zeroing neural network to uniformly solve these time-varying problems on the basis of their connections and a newly developed discretization formula. Theoretical analyses and numerical experiments, including the tracking control of PUMA560 robot manipulator, verify the effectiveness and precision of the proposed unified model.

Complex-Valued Discrete-Time Neural Dynamics for Perturbed Time-Dependent Complex Quadratic Programming With Applications

It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient for solving quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in a time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent problems. However, the research on the online solution of time-dependent complex-valued problems has been much less investigated compared to time-dependent real-valued problems. In this article, to solve the online time-dependent complex-valued QP problems subject to linear constraints, two new discrete-time neural dynamics models, which can achieve global convergence performance in the presence of perturbations with the provided theoretical analyses, are proposed and investigated. In addition, the second proposed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Moreover, computer simulation results and applications in robotics and filters are provided to illustrate the feasibility and superiority of the proposed models in comparison with the existing solutions.

New Discrete-Time ZNN Models for Least-Squares Solution of Dynamic Linear Equation System With Time-Varying Rank-Deficient Coefficient

In this brief, a new one-step-ahead numerical differentiation rule called six-instant -cube finite difference (6I CFD) formula is proposed for the first-order derivative approximation with higher precision than existing finite difference formulas (i.e., Euler and Taylor types). Subsequently, by exploiting the proposed 6I CFD formula to discretize the continuous-time Zhang neural network model, two new-type discrete-time ZNN (DTZNN) models, namely, new-type DTZNNK and DTZNNU models, are designed and generalized to compute the least-squares solution of dynamic linear equation system with time-varying rank-deficient coefficient in real time, which is quite different from the existing ZNN-related studies on solving continuous-time and discrete-time (dynamic or static) linear equation systems in the context of full-rank coefficients. Specifically, the corresponding dynamic normal equation system, of which the solution exactly corresponds to the least-squares solution of dynamic linear equation system, is elegantly introduced to solve such a rank-deficient least-squares problem efficiently and accurately. Theoretical analyses show that the maximal steady-state residual errors of the two new-type DTZNN models have an pattern, where denotes the sampling gap. Comparative numerical experimental results further substantiate the superior computational performance of the new-type DTZNN models to solve the rank-deficient least-squares problem of dynamic linear equation systems.