A Fixed-Time Projection Neural Network for Solving L₁-Minimization Problem

Two Novel Noise-Suppression Projection Neural Networks With Fixed-Time Convergence for Variational Inequalities and Applications

This article proposes two novel projection neural networks (PNNs) with fixed-time ( ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

A novel two-layer fuzzy neural network for solving inequality-constrained ℓ1-minimization problem with applications

In this paper, we propose a novel two-layer fuzzy neural network model (TLFNN) for solving the inequality-constrained ℓ1-minimization problem. The stability and global convergence of the proposed TLFNN model are detailedly analyzed using the Lyapunov theory. Compared with the existing three-layer neural network model (TLNN) recently designed by Yang et al., the proposed TLFNN model possesses less storage, stronger robustness, faster convergence rate and higher convergence accuracy. These advantages are illustrated by some numerical experiments, where it is shown that the TLFNN model can achieve a convergence accuracy of 10-13 within 5s while the TLNN model can only acquire 10-6 in 105s when some random coefficient matrices are applied. Since the linear equality-constrained conditions can be equivalently transformed into double inequality-constrained ones, some simulation experiments for sparse signal reconstruction show that the proposed TLFNN model also has less convergence time and stronger robustness than the existing state-of-the-art neural network models for the equality-constrained ℓ1-minimization problem.

A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications

In this paper, we propose a novel neurodynamic approach with predefined-time stability that offers a solution to address mixed variational inequality problems. Our approach introduces an adjustable time parameter, thereby enhancing flexibility and applicability compared to conventional fixed-time stability methods. By satisfying certain conditions, the proposed approach is capable of converging to a unique solution within a predefined-time, which sets it apart from fixed-time stability and finite-time stability approaches. Furthermore, our approach can be extended to address a wide range of mathematical optimization problems, including variational inequalities, nonlinear complementarity problems, sparse signal recovery problems, and nash equilibria seeking problems in noncooperative games. We provide numerical simulations to validate the theoretical derivation and showcase the effectiveness and feasibility of our proposed method.

Distributed continuous-time accelerated neurodynamic approaches for sparse recovery via smooth approximation to L1-minimization

This paper develops two continuous-time distributed accelerated neurodynamic approaches for solving sparse recovery via smooth approximation to L1-norm minimization problem. First, the L1-norm minimization problem is converted into a distributed smooth optimization problem by utilizing multiagent consensus theory and smooth approximation. Then, a distributed primal-dual accelerated neurodynamic approach is designed by using Karush-Kuhn-Tucker (KKT) condition and Nesterov's accelerated method. Furthermore, in order to reduce the structure complexity of the presented neurodynamic approach, based on the projection matrix, we eliminate a dual variable in the KKT condition and propose a distributed accelerated neurodynamic approach with a simpler structure. It is proved that the two proposed distributed neurodynamic approaches both achieve O(1t2) convergence rate. Finally, the simulation results of sparse recovery are given to demonstrate the effectiveness of the proposed approaches.

First/second-order predefined-time convergent ZNN models for time-varying quadratic programming and robotic manipulator application

Zeroing neural network (ZNN) model, an important class of recurrent neural network, has been widely applied in the field of computation and optimization. In this paper, two ZNN models with predefined-time convergence are proposed for the time-varying quadratic programming (TVQP) problem. First, in the framework of the traditional ZNN model, the first-order predefined-time convergent ZNN (FPTZNN) model is proposed in combination with a predefined-time controller. Compared with the existing ZNN models, the proposed ZNN model is error vector combined with sliding mode control technique. Then, the FPTZNN model is further extended and the second-order predefined-time convergent ZNN (SPTZNN) model is developed. Combined with the Lyapunov method and the concept of predefined-time stability, it is shown that the proposed FPTZNN and SPTZNN models have the properties of predefined-time convergence, and their convergence time can be flexibly adjusted by predefined-time control parameters. Finally, the proposed FPTZNN and SPTZNN models are compared with the existing ZNN models for the TVQP problem in simulation experiment, and the simulation experiment results verify the effectiveness and superior performance of the proposed FPTZNN and SPTZNN models. In addition, the proposed FPTZNN model for robot motion planning problem is applied and successfully implemented to verify the practicality of the model.

Fixed-Time Stable Neurodynamic Flow to Sparse Signal Recovery via Nonconvex L1-β2-Norm

This letter develops a novel fixed-time stable neurodynamic flow (FTSNF) implemented in a dynamical system for solving the nonconvex, nonsmooth model L1-β2, β∈[0,1] to recover a sparse signal. FTSNF is composed of many neuron-like elements running in parallel. It is very efficient and has provable fixed-time convergence. First, a closed-form solution of the proximal operator to model L1-β2, β∈[0,1] is presented based on the classic soft thresholding of the L1-norm. Next, the proposed FTSNF is proven to have a fixed-time convergence property without additional assumptions on the convexity and strong monotonicity of the objective functions. In addition, we show that FTSNF can be transformed into other proximal neurodynamic flows that have exponential and finite-time convergence properties. The simulation results of sparse signal recovery verify the effectiveness and superiority of the proposed FTSNF.

An Effective Clustering Algorithm Using Adaptive Neighborhood and Border Peeling Method

Traditional clustering methods often cannot avoid the problem of selecting neighborhood parameters and the number of clusters, and the optimal selection of these parameters varies among different shapes of data, which requires prior knowledge. To address the above parameter selection problem, we propose an effective clustering algorithm based on adaptive neighborhood, which can obtain satisfactory clustering results without setting the neighborhood parameters and the number of clusters. The core idea of the algorithm is to first iterate adaptively to a logarithmic stable state and obtain neighborhood information according to the distribution characteristics of the dataset, and then mark and peel the boundary points according to this neighborhood information, and finally cluster the data clusters with the core points as the centers. We have conducted extensive comparative experiments on datasets of different sizes and different distributions and achieved satisfactory experimental results.