Finite time dual neural networks with a tunable activation function for solving quadratic programming problems and its application

A varying-parameter fixed-time gradient-based dynamic network for convex optimization

We focus on the fixed-time convergence and robustness of gradient-based dynamic networks for solving convex optimization. Most of the existing gradient-based dynamic networks with fixed-time convergence have limited ability to resist interferences of noises. To improve the convergence of the gradient-based dynamic networks, we design a new activation function and propose a gradient-based dynamic network with fixed-time convergence. The proposed dynamic network has a smaller upper bound of the convergence time than the existing dynamic networks with fixed-time convergence. A time-varying scaling parameter is employed to speed up the convergence. Our gradient-based dynamic network is proved to be robust against bounded noises and is able to resist the interference of unbounded noises. The numerical tests illustrate the effectiveness and superiority of the proposed network.

Finite-Time Dynamic Allocation and Control in Multiagent Coordination for Target Tracking

A new finite-time dynamic allocation and control scheme is developed in this article for multiple agents tracking a moving target. Based on a competitive manner, the dynamic allocation is achieved by k-winners-take-all (k-WTA), which can be realized by a novel finite-time dual neural network with the adaptive-gain activation function. Then, a finite-time disturbance compensation-based control law is proposed for agents to conduct capturing task or return to the specified point in vigilance. The finite-time stability of the system is guaranteed through Lyapunov analysis. Finally, the efficiency of the proposed scheme is illustrated by simulations in which the situation with higher target velocity than trackers is considered.

Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

An Accelerated Finite-Time Convergent Neural Network for Visual Servoing of a Flexible Surgical Endoscope With Physical and RCM Constraints

This article designs and analyzes a recurrent neural network (RNN) for the visual servoing of a flexible surgical endoscope. The flexible surgical endoscope is based on a commercially available UR5 robot with a flexible endoscope attached as an end-effector. Most of the existing visual servo control frameworks of the robotic endoscopes or robot arms have not considered either the physical limits of the robot or the remote center of motion (RCM) constraints (i.e., the fulcrum effect). To tackle this issue, this article first conducts the kinematic modeling of the flexible robotic endoscope to achieve automation by visual servo control. The kinematic modeling results in a quadratic programming (QP) framework with physical limits and RCM constraints involved, making the UR5 robot applicable to surgical field. To solve the QP problem and accomplish the visual task, an RNN activated by a sign-bi-power activation function (AF) is proposed. The motivation of using the sign-bi-power AF is to enable the RNN to exhibit an accelerated finite-time convergence, which is more preferred in time-critical applications. Theoretically, the finite-time convergence of the RNN is rigorously proved using the Lyapunov theory. Compared with the previous AFs applied to the RNN, theoretical analysis shows that the RNN activated by the sign-bi-power AF delivers an accelerated convergence speed. Comparative validations are performed, showing that the proposed finite-time convergent neural network is effective to achieve visual servoing of the flexible endoscope with physical limits and RCM constraints handled simultaneously.