Robust combination synchronization has garnered extensive attention within the domains of science and engineering, particularly in the realm of secure communication in recent years. In contrast to traditional synchronization control architecture (TSCA), the introduction of multiple variables and intricate combination methods in combination synchronization control architecture (CSCA) can significantly increase the complexity of decryption and improve the security and confidentiality of signal transmission. Meanwhile, due to the ubiquity of time-varying external interference, the combination synchronization results of existing methods may not be ideal. In view of these challenges, in this article, we design a controller based on the integration-enhanced zeroing neural network (IEZNN) model to obtain the goal of realizing robust combination synchronization, together with the rigorous theoretical analysis on the convergence performance of the IEZNN-based controller and the conventional zeroing neural network (CZNN)-based controller in the cases of zero noise, constant noise and dynamic bounded noise. In addition, the varying parameter zeroing neural network (VPZNN)-based controller is used to further illustrate the superiority of the IEZNN-based controller. The simulation experiment results not only further validate the theoretical analyses, but also demonstrate that the IEZNN-based controller can realize chaotic combination synchronization with the superior convergence performance even in the existence of the time-varying external disturbances. In the end, the CSCA encapsulated with the IEZNN-based controller is utilized for the chaotic combination synchronization to realize the purpose of secure communication by using Matlab/Simulink tool.

In order to better adapt to the needs of practical scenarios, multiagents task allocation systems need to be able to select winners in the shortest possible time under external interference. Therefore, this article proposes a finite time and robust $k$-winners-take-all (FTR-$k$WTA) neural network, by introducing a time-varying learning rate and a versatile activation function into the $k$WTA neural network. Compared with existing $k$WTA neural networks, this network has faster finite-time convergence speed and noise suppression ability. The global convergence, finite-time convergence, and robustness of the proposed network have been demonstrated theoretically. Finally, these performances of the FTR-$k$WTA neural network are further validated through simulation results. In addition, the multiagents system is simulated using E-puck robots on the CoppeliaSim platform, serving to confirm the efficacy of the FTR-$k$WTA neural network.

Natural language programming of robotic systems presents significant challenges in bridging high-level intent with low-level motion planning, particularly for redundant manipulators in artistic or spatially constrained tasks. We present BeetleBrush, a novel LLM-powered robotic drawing framework that combines large-scale language understanding with bio-inspired optimization for trajectory execution. Natural language prompts are processed using Google Gemini 2.5 Flash within a Retrieval-Augmented Generation (RAG) system enhanced by a curated database of over 200 drawing examples. The resulting stroke sequences are translated into target end-effector trajectories, which are executed using a 7-DOF KUKA manipulator through an enhanced Beetle Antennae Search (BAS) algorithm operating in forward kinematics space-circumventing the need for analytical inverse kinematics. Our system achieves accurate, safe, and expressive robot drawings with real-time performance and high workspace compliance. Across 12 representative prompts of varying complexity, BeetleBrush achieved mean end-effector errors of 0.0048-0.0051 meters and RMSE values below 0.0051 meters in most cases, with maximum errors under 0.0173 meters. The system also exhibited stable convergence behavior and successfully executed 94.4% of strokes across tasks, including geometrically constrained figures like cubes, cones, and composite scenes. Direct quantitative comparison against Jacobian pseudo-inverse IK and Particle Swarm Optimization baselines within the same simulation confirms BAS superiority in convergence reliability (100% vs. 75% for IK) and computational efficiency (14.2 ms vs. 187 ms per waypoint for PSO). A rigorous ablation study quantifies the individual contributions of the RAG module, L & eacute;vy flight, and adaptive sensing decay. A hyperparameter sensitivity analysis confirms robustness within a +/- 50% band around the chosen parameter values, and a sim-to-real perturbation analysis under modeled joint noise and friction demonstrates that RMSE remains below 9 mm under realistic physical disturbances. BeetleBrush demonstrates how LLM-guided generation and bio-inspired control can be effectively integrated for robust, intuitive, and geometry-aware robot programming.

Harmonic noise frequently arouses by the disturbances in industrial applications, which would be a great threat to the security, stability and service life of equipment in some large and critical facilities, especially in power systems. Therefore, finding away to resist harmonic noise is highly important. The zeroing neural networks (ZNN) have lately gained exceptional success in solving time-varying problems (TVP) as a result of its efficiency. Inspired by the effectiveness of ZNN and the dynamic system model design principles in control theory, we initially develop a coupled anti-mixed noise ZNN (AMNZNN) model that can resist the combination of single harmonic and non-harmonic noise (e.g., random noise). Then, an extended AMZNN model is further designed to remove the combination of multi-harmonic noise and non-harmonic noise. Additionally, comparisons among original ZNN (OZNN), integration-enhanced ZNN (IEZNN), harmonic-noise- tolerant ZNN (HNTZNN) and the proposed AMNZNN for time-varying matrix inversion (TVMI) under the mixture of harmonic noise and random noise are experimented to demonstrate the proposed AMNZNN model's superior ability in resisting mixed noise. Finally, by applying the proposed extended formalism to power systems and microphone arrays in denoising, the effectiveness of the proposed method to resist multi-harmonic and random noises is further verified in scientific applications.

Various types of noise interference often challenge the solution of discrete time-varying linear matrix problems with boundary constraints in practical engineering applications. To address this issue, this paper proposes a Taylor-type direct-discrete-time integral noise-immune recurrent neural network (TD-IRNN) model. Specifically, the model is constructed by transforming the bounded discrete linear matrix problem into a unified discrete matrix formulation and incorporating an error accumulation term during the design process. The proposed TD-IRNN model not only eliminates the need for continuous-environment conversion but also significantly enhances its noise immunity. Theoretical analysis demonstrates that the model exhibits excellent convergence and stability under different noise conditions. Numerical experiments and a robotic manipulator trajectory tracking experiment further validate the effectiveness and practical applicability of the TD-IRNN model in complex environments.

Discrete time-varying linear matrix problems (DTVLMP) play an important role in the field of artificial intelligence and control engineering. This article presents a direct solution to the DTVLMP based on Taylor difference discrete time-varying recurrent neural network (TD-DRNN) model. First of all, the TD-DRNN operates in a directly discrete time-varying framework, avoiding the need to build a theoretical foundation from a continuous time-varying recurrent neural network (RNN) model. Then, the theoretical properties of the TD-DRNN have been rigorously analyzed, demonstrating both its convergence and accuracy. These results show that the new TD-DRNN model has remarkable computational performance. Furthermore, the effectiveness and versatility of the TD-DRNN model have been substantiated through a numerical simulation and the application of two robotic trials.

Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To overcome these deficiencies, this paper proposes a fuzzy integral direct discrete recurrent neural network (FITDRNN) model. The FITDRNN model incorporates an integral term to counteract noise interference and employs a fuzzy logic system for dynamic adjustment of the integral parameter magnitude, thereby further enhancing its noise resistance. Theoretical analysis, combined with numerical experiments and robotic arm trajectory tracking experiments, verifies the convergence and noise resistance of the proposed FITDRNN model.

The time-varying (TV) problems frequently happen in various practical engineering fields. As for their solution, most neural network models are based on the classical gradient-based neural network (CGNN) with an evident lagging error, which is tailored for time-independent problems. Considering the wide range of applications of gradient-based algorithm in many fields, in this article, we propose an improvement to the CGNN model based on the Lyapunov control theory, resulting in an adaptive robust gradient-based recurrent neural network (ARG-RNN), which is demonstrated that it is an effective neural solver for the TV problems in theory and also substantiated by following the simulated real-valued and complex-valued linear matrix equations solving experiments and an angle of arrival (AoA) location application. Additionally, most neural network models are developed for noise-free environments, while noise is often unavoidable in practical applications. Therefore, the presented ARG-RNN is also verified to be capable of obtaining an exact solution even in the face of external constant noise, linear TV noise, or bounded random noise by the noise-tolerant experiments and comparisons.

Effectively enhancing the trajectory stability and accuracy of robots has become a key research focus in robotic automation. This paper primarily investigates the optimization of robot motion trajectories for stability and precision, and we propose an Integral-Enhanced Sliding Mode Surface Zeroing Neural Network (IESMSZNN). This network leverages the sliding mode surface with integral control to resist noise and achieve rapid stabilization. Furthermore, a Complex-Valued Noise-Resistant Finite-Time Convergent Zeroing Neural Network (CNFZNN) is introduced as the reaching law for the sliding mode system. Theoretical analysis confirms that the proposed model possesses strong robustness and favorable convergence performance. Numerical experiments indicate that, compared with the conventional Zeroing Neural Network (CZNN), the Integral-Enhanced Zeroing Neural Network (IEZNN), and the Sliding Mode Surface Zeroing Neural Network (SMSZNN), the IESMSZNN exhibits smaller fluctuations under various noise conditions and can achieve stable convergence within 2 seconds. The IESMSZNN effectively improves noise resistance, providing a novel approach for sliding mode noise-resilient controllers. Finally, experimental validations demonstrate that the IESMSZNN can effectively withstand four common noise types while ensuring rapid and stable convergence, thereby meeting the accuracy and stability requirements of advanced robot applications.

During the process of the general practical applications and scientific researches, time varying issues are an inescapable challenge to be tackled. In this article, a pre-defined finite-time zeroing neural networks (PDFT-ZNN) is devoted to solve the linear time-variant matrix equation (TVME) E(t)X(t)G(t)=D(t) within a finite time (FT), which contrasts with the general ZNN (G-ZNN) models with relatively long global convergence time. Moreover, the proposed PDFT-ZNN model’s convergence time could be calculated in advance by adhering to the designed system parameters; this has nothing to do with the model’s initial state. Additionally, after the convergence analysis, if the solution error is relative small, the simple and effective method is to introduce a linear item to accelerate the convergence speed, in comparison with only the power-type ZNN models. Theory-based analysis and simulation-based results further validate that, the neural state solved by the presented FT-ZNN model can reach the theory-based solution of E(t)X(t)G(t)=D(t) within the pre-defined finite time.

Sparrow Algorithm as a New Swarm Intelligence Search Algorithm, the sparrow algorithm has good optimization ability, but in complex environments, it still has certain limitations, such as weak learning ability. Therefore, this paper proposes a learning sparrow search algorithm for non-uniform search(Sparrow search algorithm with non-uniform search, NSSSA). A learning behavior selection strategy is proposed, and saltation learning and a random walk learning are introduced respectively.To a certain extent, the algorithm avoided alling into the local optimum, and a non-uniform variable spiral search is proposed to balance the development and search capabilities of the algorithm. In the experimental simulation, the effectiveness of the NSSSA algorithm is verified by using the benchmark function, and it is tested on the CEC 2013 test set. Compared with the algorithms with better performance in recent years, the results show that the NSSSA algorithm has better universality . Finally, the NSSSA algorithm is applied to the WSN coverage optimization problem. The results show that NSSSA achieves more than 90% and 96% coverage on the two models of 50×50 and 100×100, respectively, which verifies the practicability of the algorithm.

In order to improve the global search ability and easy to fall into local extrema, we propose a modified crow search algorithm (ISA) based on differential variation perturbation factor and dynamic recurrence rules of model parameters. Introduce the differential variation perturbation factor to accelerate the information exchange and improve the convergence rate, and then introduce the model parameter dynamic recurrence rule to improve the perception probability and flight length to balance the global search and local search. The experimental results of the ablation experiments on two engineering optimization design problems show that the optimization performance of the improved crow search algorithm improves significantly, which proves the effectiveness and correctness of the improved method.

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments.

It is well-known that, the classical gradient-descent-based neural network (CGNN) model is used widely for the time-invariant problem solving. However, it is an extremely common problem for the time varying cases in the practical engineering applications, while the CGNN effective neural solver for the time-variant problems. For this reason, in this article, an adaptive GNN (AGNN) is presented for the linear time variant matrix equation (LTVME) on-line solving based on Lyapunov theory. Theoretical analysis already verified that the presented AGNN model could achieve the correct state solution effectively. The simulated experiment results further validate that the state solution of the AGNN model could be convergent to the correct solution of the solved time variant problems in theory.

The time-variant Sylvester equation (TVSE) plays a highly crucial role in many areas of scientific research and engineering applications. Recently, zeroing neural network (ZNN) has been prevailed as an effective solution for time-variant problem. However, the majority of the existing ZNN solution schemes for TVSE are either only considered in noiseless environments or are unable to converge in a finite amount of time, and while there is a pressing need for effective and noise-resisting ZNNs to fulfill real-time applications’ requirements in the actual world. For this reason, inspired by the advantages offered by super-twisting algorithm (STA), being a well-accepted second order sliding mode method, this paper introduces STA into ZNN and establishes a novel STZNN model for TVSE solving. Actually, the intrinsic properties of STA, such as finite-time convergence and anti-noise robustness, are perfectly in line with what an efficient and noise-resisting ZNN model desired to be. Hence, the STZNN model can realize a much quick convergence time and a much great resistance against noise. Moreover, rigorous theoretical analyses on the case of zero noise, constant noise and dynamic bounded noise are conducted, and the illustrative verification not only verifies the STZNN’s convergence property, validates its superior ability in convergence time and noise resisting compared to the gradient-based neural network (GNN), the conventional ZNN (CZNN) model and the integration-enhanced ZNN (IEZNN) model, but also shows the STZNN model’s capability in addressing moving localization problems based on angle of arrival (AoA) and time difference of arrival (TDOA).

The redundant manipulator as a ubiquitous and essential component of robots, acts as a momentous role in mechanized production. The motion control of a redundant manipulator is an essential problem that must be handled. Consequently, for the repetitive motion control of redundant manipulators, a recurrent neural network (RNN) model for the double-index (DI) scheme is researched in this paper. The DI scheme sets the minimum kinetic energy (MKE) and minimum joint-angle offset (MJAO) as optimization indexes, for which the time-dependent weights are designed, and takes the dynamic equations of redundant manipulators and joint limit constraints into consideration as well. Then, the DI scheme is reformulated as a quadratic programming (QP) problem. Besides, the RNN model based on the iteration of related parameters is derived to solve the QP problem, through which joint data (i.e., joint angles, joint velocities, and joint accelerations) are obtained to drive the motion of the redundant manipulator. To verify the effectiveness of the DI scheme for motion control of redundant manipulator, simulation results of the DI scheme solved by the RNN model, the minimum acceleration norm (MAN) scheme and MKE scheme are compared.

Traditional gradient-based neural networks may fall into local minima, and because these networks involve with lengthy iteration process, they are not fast enough. By the generalized-inverse method, the least squares solution with the smallest 2-norm can be obtained. For traditional neural networks based on generalized-inverse method, the weights from the hidden layer to the output layer and the biases are generated by a random approach; the weights from the hidden layer to the output layer are calculated with the aid of generalized-inverse method. In triple generalized-inverse neural network (TGINN) proposed in this paper, all the weight matrixes from one layer to another are calculated with the aid of generalized-inverse method, as well as for biases of neurons in the hidden layer. Comparison experiments between TGINN and other models are carried out. and the experimental results illustrate the superiority of the proposed TGINN.

TSP(1,2) problem is a special case of the travelling salesperson problem which is NP-hard. Many heuristics including evolutionary algorithms (EAs) are proposed to solve the TSP(1,2) problem. However, we know little about the performance of the EAs for the TSP(1,2) problem. This paper presents an approximation analysis of the (1+1) EA on this problem. It is shown that both the (1+1) EA and (µ + λ) EA can obtain 3/2 approximation ratio for this problem in expected polynomial runtime O(n3) and O ((µ/λ)n3 + n) , respectively. Furthermore, we prove that the (1+1) EA can provide a much tighter upper bound than a simple ACO on the TSP(1,2) problem.

It is a challenge problem to stably control the well-known Lorenz system with uncertain parameters because of its nonlinearity and singularity. In this paper, by combining Zhang dynamics (ZD) and gradient-algorithm, a novel Zhang-Gradient (ZG) controller is designed and developed for solving the controlling problem of the uncertainty Lorenz system. In order to improve computing efficiency, the stochastic parallel gradient descent algorithm is also introduced to perform an incremental adjustment of the unknown parameters for the uncertain Lorenz system. The presented theoretical analysis in this paper shows that our such presented method could conquer the possible singularity which is a difficult problem in typical backstepping controller design. The computer simulation results exhibit that, the controlled system can be stable globally and the tracking error converges to zero asymptotically, which are further demonstrate the effectiveness and feasibility of our presented ZG controller.

Breast cancer has become one of the leading causes of death in female population due to its high morbidity and mortality. However, the treatment options for benign or malignant tumors are different, which makes the diagnosis of breast cancer important. In this paper, the subset method is proposed to improve the single-output Chebyshev-polynomial neural network (SOCPNN), and the modified SOCPNN has a 100.00% testing accuracy in pattern classification on the Wisconsin breast cancer dataset. Specifically, the subset method generates the optimal number of cross-validation folds and constructs the initial structure of the modified SOCPNN automatically and rapidly, with a group of basis functions based on Chebyshev-polynomials exploited to activate the neural network. In addition, the weights of the hidden-layer neurons are directly determined by the weights-direct-determination (WDD) method. Besides, the optimal structure of the neural network is determined by a growing method. Moreover, to improve the generalization performance, the multi-fold cross-validation algorithm is exploited in the modified SOCPNN. Finally, comparative experiments on the Wisconsin breast cancer dataset are conducted and the results show that the modified SOCPNN has higher accuracy in classification of breast cancer on this dataset compared to the traditional machine learning algorithms.