Inverse-Free Discrete ZNN Models Solving for Future Matrix Pseudoinverse via Combination of Extrapolation and ZeaD Formulas

Inverse-free zeroing neural network for time-variant nonlinear optimization with manipulator applications

In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm.

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.

Robust neural dynamics with adaptive coefficient applied to solve the dynamic matrix square root

Zeroing neural networks (ZNN) have shown their state-of-the-art performance on dynamic problems. However, ZNNs are vulnerable to perturbations, which causes reliability concerns in these models owing to the potentially severe consequences. Although it has been reported that some models possess enhanced robustness but cost worse convergence speed. In order to address these problems, a robust neural dynamic with an adaptive coefficient (RNDAC) model is proposed, aided by the novel adaptive activation function and robust evolution formula to boost convergence speed and preserve robustness accuracy. In order to validate and analyze the performance of the RNDAC model, it is applied to solve the dynamic matrix square root (DMSR) problem. Related experiment results show that the RNDAC model reliably solves the DMSR question perturbed by various noises. Using the RNDAC model, we are able to reduce the residual error from 10$$^1$$ 1 to 10$$^{-4}$$ - 4 with noise perturbed and reached a satisfying and competitive convergence speed, which converges within 3 s.