Existing computational methods for the $k$ -winners-take-all ( $k$ WTA) operations often suffer from limitations in eliminating lagging errors, high computational complexity, and weak robustness. To deal with these challenges, we propose an integral-enhanced adaptive gradient neural network (IAGNN) for $k$ WTA. We demonstrate that the IAGNN integrates an adaptive coefficient to eliminate lagging errors while retaining an $O(n^{2})$ computational complexity. We proved the Lyapunov stability and robustness of the IAGNN. We provide a numerical simulation, and the results demonstrate the stability and robustness of the IAGNN. Furthermore, we implement the IAGNN in a multirobot tracking system for competitive allocation coordination, and the results demonstrate the operational feasibility and noise resistance of the IAGNN.

Memristor crossbar array (MCA) is a computing-in-memory (CIM) module for computational acceleration. However, conventional read-write (R-W) circuits for MCA rely heavily on external components and have shortcoming in long writing times. To address these issues, we propose a parallel R-W circuit with a fast amplitude-adaptive matching (AAM) scheme. The fast AAM scheme is designed to accelerate time of writing memristors in MCA by adaptively adjusting the writing voltage to match an optimal amplitude. The architecture of parallel R-W circuit are outlined with the implementation of R-W processes. The design principles of parallel R-W unit, fast AAM unit, and associated control logic are described for analyzing their functions within the circuit. By integrating the parallel R-W circuit with MCA, a computing block is leveraged in a neural network for classification tasks. The experimental results demonstrate that the neural network with multiple computing blocks maintains high accuracy across various datasets (over 80%). Furthermore, the proposed AAM scheme achieves an average 54% reduction in writing time compared to that one without AAM scheme. Compared to the pulse-width scheme, the parallel R-W circuit exhibits an average$3.05\times $speedup in adjusting a$5\times 5$MCA, and the speedup efficiency is higher as the increases of MCA size.

In this article, we propose a fuzzy adaptive network (FAN) with learnable parameters for mixed-integer optimization. Specifically, by leveraging a recurrent network to infer the discretization parameters, the FAN is implemented in an easy-to-implement discrete-time format. FAN possesses the dynamic behavior of a high-precision numerical differential rule and maintains a simple network structure. In addition, a fuzzy mechanism is incorporated to adjust the step size. Sufficient conditions are derived such that the proposed FAN is globally exponentially convergent to a Karush–Kuhn–Tucker point. In the presence of nonconvexity in objective functions or constraints, multiple FANs operate concurrently in a hybrid intelligent algorithm. Finally, multiple comparative experiments are conducted to demonstrate the superiority of the proposed FAN in terms of time efficiency and solution quality.

To improve the acceleration performance, a hybrid state-triggered discretization (HSTD) is proposed for the adaptive gradient neural network (AGNN) for solving time-dependent linear equations (TDLEs). Unlike the existing approaches that use an activation function or a time-varying coefficient for acceleration, the proposed HSTD is uniquely designed from a control theory perspective. It comprises two essential components: adaptive sampling interval state-triggered discretization (ASISTD) and adaptive coefficient state-triggered discretization (ACSTD). The former addresses the gap in acceleration methods related to the variable sampling period, while the latter considers the underlying evolutionary dynamics of the Lyapunov function to determine coefficients greedily. Finally, compared with commonly used discretization methods, the acceleration performance and computational advantages of the proposed HSTD are substantiated by the numerical simulations and applications to robotics.

The trust-region method and projection neural networks are two branches of optimization approaches with different operational principles and characteristics. In this article, a trust-region projection neural network (TRPNN) is proposed by integrating the trust-region method and projection neural networks. TRPNN is a discrete-time neurodynamic optimization model that inherits the exploration-exploitation capability of the trust-region method and the local search capability of projection neural networks. TRPNN is theoretically proven to be convergent to a Karush-Kuhn-Tuchker (KKT) point of nonlinear programming problems. The efficacy of TRPNNs leveraged in a collaborative neurodynamic framework is numerically demonstrated for global optimization in the presence of nonconvexity in objective functions or constraints.

Due to the significant role of sea ice in the Arctic-related research, developing high-precision and robust Arctic sea ice extraction techniques for multi-source remote-sensing images encounters a great challenge. In the light of the constrained energy minimization scheme, this article provides a generalized complex-valued constrained energy minimization (GCVCEM) scheme for the Arctic sea ice extraction with strong robustness and accessible implementation. Given the fact that the image extraction process is easily disturbed by noise in real-life application scenarios, a modified Newton integration (MNI) neural algorithm with the noise-tolerance ability and high extraction accuracy is proposed to aid the GCVCEM scheme. Its key idea is to add an error integration feedback term on the basis of the Newton–Raphson iterative (NRI) algorithm to resist noise perturbation on the solution process of the GCVCEM scheme for high-precision and robust extraction of the Arctic sea ice. Besides, the corresponding convergence analyses and robustness proofs on the proposed MNI neural algorithm are furnished. To evaluate the extraction performance of the proposed MNI neural algorithm, multiple comparative experiments with different sea ice observation images and different noise workspaces are performed. Both the visualized and quantitative experimental results substantiate the superiorities of the proposed MNI neural algorithm aided the GCVCEM scheme for the Arctic sea ice extraction.

Currently, the Newton–Raphson iterative algorithm has been extensively employed in the fields of basic research and engineering. However, when noise components exist in a system, its performance is largely affected. To remedy shortcomings that the conventional computing methods have encountered in a noisy workspace, a novel modified Newton integration (MNI) algorithm is proposed in this article. In addition, the steady-state error of the proposed MNI algorithm is smaller than that of the Newton–Raphson algorithm under a noise-free or noisy workspace. To lay the foundations for the corresponding theoretical analyses, the proposed MNI algorithm is first converted into a homogeneous linear equation with a residual term. Then, the related theoretical analyses are carried out, which indicate that the MNI algorithm possesses noise-tolerance ability under various noisy environments. Finally, multiple computer simulations and physical experiments on robot control applications are performed to verify the feasibility and advantage of the proposed MNI algorithm.

In this article, the existing approaches, including numerical algorithms as well as neural networks to solve dynamic linear matrix equations, have been presented and reviewed. Specifically, the conventional gradient recurrent neural networks (CGRNNs) and the conventional zeroing neural networks (CZNNs) are successively provided to solve the dynamic problems and linear matrix equations, both of which manifest inherent limitations during the solving procedures. To remedy the drawbacks on convergence time, nonzero residual error, and large computational load of the traditional models, an adaptive gradient recurrent neural network (AGRNN) to solve dynamic linear matrix equations is proposed. This proposed inversion-free model possesses rapid convergence rate and accurate calculated solutions. Moreover, theoretical analyses guarantee the advantages of the AGRNN compared with the CGRNN and the CZNN to solve dynamic linear matrix equations. Finally, three numerical experiments, and applications to a PUMA 560 robot motion planning and a mobile subject localization based on angle-of-arrival technique are implemented to testify the advantages of the AGRNN.

A dynamic complex-valued matrix pseudoinversion (DCVMP) is encountered in some special environments, where the system parameters contain the dynamic, magnitude, and phase information. Currently, most of the existing models are employed to the DCVMP under a noise-free workspace. However, the noise perturbation is unavoidable in the practical application scenarios. Therefore, the motivation of this article is to design a computational model for the DCVMP with strong robustness and high-precision computing solutions. To this end, a modified Newton integration (MNI) neural algorithm is proposed for the DCVMP with noise-suppressing ability in this article. Besides, the corresponding convergence proofs on the MNI neural algorithm are provided. Furthermore, the numerical simulations and an application to the estimation of mobile object localization, are demonstrated to illustrate the superiority of the MNI neural algorithm.

Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this study, a nonconvex and bound constraint zeroing neural network (NCZNN) model is designed and theorized to solve the time-varying complex-valued QP with linear equation constraint. Besides, we construct several new types of nonconvex and bound constraint complex-valued activation functions by extending real-valued activation functions to the complex domain. Subsequently, corresponding simulation experiments are conducted, and the simulation results verify the effectiveness and robustness of the proposed NCZNN model. Moreover, the model proposed in this article is further applied to solve the issue of small target detection in remote sensing images, which is modeled to QP problem with linear equation constraint by a serial of conversions based on constrained energy minimization algorithm.