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The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the "infinite memory" effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model's ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. [ABSTRACT FROM AUTHOR]

To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed. [ABSTRACT FROM AUTHOR]

Radio Frequency IDentification (RFID) Network Planning (RNP) is the problem of placing RFID readers in a working area where a tag is interrogated by at least one reader and at the same time satisfies some constraints such as minimum number of placed readers, minimal interference, and minimal outside coverage. The RNP optimization has been proven NP-hard; thus, natural-inspired approaches are often used to find the optimal solution. The paper proposes an energy-efficient RNP approach in which the positions of placed readers are optimized by a Hopfield network, and the energy efficiency is achieved through a placement area restriction technique. A mechanism of redundant reader elimination is also added to minimize the number of placed readers. Simulation results show that the Hopfield network-based energy-efficient RNP approach achieves the maximum tag coverage and energy efficiency by reducing interference, outside coverage, and the number of placed readers. [ABSTRACT FROM AUTHOR]

This paper investigates the impulsive stability analysis issues of discrete-time positive singular systems with time delay. First, the paper addresses the positivity problem of the system by providing sufficient conditions. Next, a new method based on state transformations is presented to derive a new delay-dependent criterion for the exponential stability of impulsive positive singular systems. Finally, the effectiveness of the proposed conditions is validated through three numerical examples. [ABSTRACT FROM AUTHOR]

Logical gates have been used in implementation of logic sequential and combinational circuits especially in computers, DSPs and microprocessors. They are mostly fabricated based on CMOS technology that provides a few nano-seconds of delay for each digital gate. Due to limitations in more scaling CMOS transistors and cause of short channel effects, some engineers and researchers believe that there is a huge demand for new devices and fabrication technologies to produce faster logic gates. In this paper, a new architecture for NAND gate is presented which operates based on mechanical resonance of a network of weakly coupled resonators that resonate in radio frequencies. This design is achieved by employing the associative memory property of Hopfield neural networks and the theory of weakly coupled resonators. The main advantage of the proposed design is in its capability to reach out delay times of the order of 1 nano-seconds or even less. One solution to decrease the delay time can be increasing the resonance frequency of resonators which are processing elements of resonators network. In this paper just the new idea of implementation NAND gate based on weakly coupled RF MEMS resonators is presented and evaluated. Other criteria like gate power consumption, effects of temperature, fan in, fan out and noise margin are not discussed. Regarding the rapid growth in MEMS technology, resonators with super high frequency (SHF 3–30 GHz) are now available and those with Extremely High frequency (EHF 30–300 GHz) will soon be in market which enables the presented design to achieve higher speeds. In addition, mechanical resonators are more fault tolerant than CMOS circuits when utilized in harsh environments which exposed to ionic beams or electron beam radiations. In space applications, the satellite and payload are exposed to huge bombardments of space electrons and ions beams. So, the proposed NAND gate can be a good solution for enhancing reliability of devices and systems exposed to space radiations. [ABSTRACT FROM AUTHOR]

Using the Neural Networks to predict solar harvestable energy would contribute to prolonging the duration of the effective operation and thus less consumption in solar-harvesting sensor nodes. The NNs with higher prediction accuracy have the longest effective operation. Till now, the NNs that use the zenith angle function as input have been utilized with only two terms. This paper shows the advantages of using a multi-term zenith angle function on the energy management in the nodes. To this end, this paper considers two, three, and four terms for the function of the zenith angle. The results showed that the case of four terms has the lowest prediction mistakes on average (0.83%) compared to (2.13% and 1.75%) for the cases of two and three terms, respectively. This is followed by a reduction in energy consumption in favor of four terms case. For one month simulation period with hourly prediction, the sensor node worked at the higher consumption mode (M2) in the case of four terms 4 hours less than three terms and 7 hours less than two terms case. Thus, increasing the number of terms in the zenith angle function leads to higher accuracy and less energy consumption. [ABSTRACT FROM AUTHOR]

The growing utilization of neural networks has led to a heightened focus on the hardware implementation of such networks. Security concerns associated with these implementations pose a significant challenge in this regard. Among these problems, the vulnerability of these networks against side-channel attacks such as power attacks can be mentioned. This paper presents a technique to enhance the resilience of hardware implementations of neural networks, particularly Hopfield neural networks, to mitigate the risks posed by power attacks. In addition to the fact that the proposed method makes it impossible to attack the network, it also reduces the power consumption of the entire circuit by reducing the leakage currents. The simulation results demonstrate that the proposed approach also achieves about a 10% reduction in energy consumption while concurrently improving the accuracy of the implemented associative memory by 1.1%. [ABSTRACT FROM AUTHOR]

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some suffcient conditions for ensuring pth moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coeffscients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the input-to-state stability (ISS) and uniform stability for impulsive nonlinear systems with delayed impulses, where delays are flexible between two consecutive impulsive instants. Illustrating effects caused by delays, concepts of generalised average impulsive delay and generalised reverse average impulsive delay are introduced, and more applicable in practice. Moreover, sufficient conditions for stability properties are formulated with destabilising and stabilising impulses through a general candidate ISS-Lyapunov function and the generalised conditions. It is shown that the double effects of delays in impulses (i.e. stabilising an initial unstable system, or contrarily, destabilising an initial stable system) coincide with the existing results using the exponential candidate ISS-Lyapunov function. Finally, two examples are provided to demonstrate our developed techniques. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply and time delays is studied. Compared to the apoptosis process of tumor cells, there is a time delay in the process of tumor cell division. The cells inside the tumor obtain nutrient σ(r,t) through blood vessels, and the tumor attracts blood vessels at a rate proportional to α(t). So, the boundary value condition ∂σ ∂r + α(t)(σ − ψ(t)) = 0,r = R(t),t > 0, holds on the boundary, where the function ψ(t) is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that ψ(t) is a periodic function. Sufficient conditions for the global stability of zero steady state are presented. Under certain conditions, we prove that there exists at least one periodic solution to the model. The results are illustrated by computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]

This paper proposes a new H ∞ static output feedback control method to address the congestion control problem in transmission control protocol networks using active queue management routers. Based on linear matrix inequality optimization, this method determines a static output feedback control law to minimize the H ∞ norm of the transfer function between the controlled queue length of the buffer and the exogenous disturbance affecting the available link bandwidth. A linear matrix inequality formulation is presented as a sufficient condition to guarantee the closed-loop system's asymptotic stability while maintaining disturbance rejection within a specified level, regardless of round-trip time delays. The proposed robust static output feedback control eliminates the need to measure or estimate all system states, thus simplifying practical implementation. The effectiveness of the proposed design method is demonstrated by applying it in a practical process, as illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

Economic growth is resulting in serious environmental problems. Effectively establishing an economic growth model that considers environmental pollution is an important topic. To analyze the interplay between economic growth and environmental pollution, a fractional-order time-delayed economic growth model with environmental purification is proposed in this paper. The established model considers not only the environment and economic production but also the labor force population and total factor productivity. Furthermore, the asymptotic stability conditions and parameter stability interval are provided. Finally, in numerical experiments, the correctness of the theory is verified. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings. [ABSTRACT FROM AUTHOR]

The object of this study is the assessment of the level of enterprise bankruptcy risk. It is a critical component in assessing the financial condition of an enterprise, and also serves as an indicator that allows the management team to reduce potential risks and develop their own strategies to strengthen the financial condition of the enterprise. One of the most challenging aspects of bankruptcy forecasting is the complex financial situations of bankrupt companies. By accurately predicting the risk of bankruptcy, businesses can take preventive measures to mitigate financial difficulties and ensure long-term sustainability. Previous methods, such as Altman’s Z-score, are not accurate enough, as presented in the study. The paper investigates a modern approach to bankruptcy prediction based on a neural network with complex neural elements, namely neural arithmetic logic units (NALUs) and a custom phasing layer. This layer can process complex raw numerical values, such as financial indicators relevant to the analysis of a company’s bankruptcy. Compared to Altman’s Z-score, the developed method demonstrates a better F1 score in bankruptcy classification (48 %). On the raw data, the neural network demonstrates an improvement in the F1 score by about 40 % compared to the classical multilayer perceptron (MLP) with linear layers and nonlinear activation functions. A modern replacement for ReLU called Mish was used, which achieves better generalization. It was also assumed that the addition of new neural elements, which provide the neural network with arithmetic capabilities, contributes to the performance of processing non-normalized input data. This work highlights the importance of using advanced neural network architectures to improve the accuracy and reliability of forecasting in financial risk assessment. Using the parameters presented in the study, managers of enterprises will be able to more accurately assess the risk of bankruptcy. [ABSTRACT FROM AUTHOR]

This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction–diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach. • Our study enriches the related research of semi-Markov RDSs. The obtained results guarantee the finite-time synchronization of semi-Markov RDSs, which is more effective and practical than asymptotic synchronization. • This paper proposes a novel asynchronous boundary control scheme, for the synchronization of semi-Markov RDSs. Compared with existing ones, our control scheme has obvious advantages in realizability and economy. • Based on the existing papers, in the designed controller, a constant is introduced, such that the intense chatter of controller could be reduced. • For the considered systems and designed controller, a new finite-time stability lemma is proposed, which enables the derivation of a finite-time synchronization criterion and a related corollary of this paper. [ABSTRACT FROM AUTHOR]

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed way. Further, synaptic plasticity in the brain depends only on information local to synapses. Deep networks, on the other hand, typically use non-local learning algorithms and are trained in an offline, non-noisy, independent, identically distributed setting. Understanding how neural networks learn under the same constraints as the brain is an open problem for neuroscience and neuromorphic computing. A standard approach to this problem has yet to be established. In this paper, we propose that discrete graphical models that learn via an online maximum a posteriori learning algorithm could provide such an approach. We implement this kind of model in a neural network called the Sparse Quantized Hopfield Network. We show our model outperforms state-of-the-art neural networks on associative memory tasks, outperforms these networks in online, continual settings, learns efficiently with noisy inputs, and is better than baselines on an episodic memory task. Brains and neuromorphic systems learn with local learning rules in online-continual learning scenarios. Designing neural networks that learn effectively under these conditions is challenging. The authors introduce a neural network that implements an effective, principled approach to local, online-continual learning on associative memory tasks. [ABSTRACT FROM AUTHOR]

Linear assignment problems hold a pivotal role in combinatorial optimization, offering a broad spectrum of applications within the field of data sciences. They consist of assigning "agents" to "tasks" in a way that leads to a minimum total cost associated with the assignment. The assignment is balanced when the number of agents equals the number of tasks, with a one-to-one correspondence between agents and tasks, and it is and unbalanced otherwise. Additional options and constraints may be imposed, such as allowing agents to perform multiple tasks or allowing tasks to be performed by multiple agents. In this paper, we propose a novel framework that can solve all these assignment problems employing methodologies derived from the field of statistical physics. We describe this formalism in detail and validate all its assertions. A major part of this framework is the definition of a concave effective free energy function that encapsulates the constraints of the assignment problem within a finite temperature context. We demonstrate that this free energy monotonically decreases as a function of a parameter β representing the inverse of temperature. As β increases, the free energy converges to the optimal assignment cost. Furthermore, we demonstrate that when β values are sufficiently large, the exact solution to the assignment problem can be derived by rounding off the elements of the computed assignment matrix to the nearest integer. We describe a computer implementation of our framework and illustrate its application to multi-task assignment problems for which the Hungarian algorithm is not applicable. [ABSTRACT FROM AUTHOR]

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples. [ABSTRACT FROM AUTHOR]

The electro-hydraulic servo system has advantages such as high pressure, large flow, and high power, etc., which can also realize stepless regulation, so it is widely used in many engineering machineries. A linear model is sometimes only a simple approximation of an idealized model, but in an actual system, there may be nonlinear and transient variation characteristics in the systems. Coupling is reflected in the fact that the components or functional structures implemented by each system used for the design of hydraulic systems are not completely or independently related to each other, but affect each other. The nonlinear clearance between the actuator and the load reduces the control accuracy of the system and increases the impact, thus losing stable working conditions. In the paper, based on the nonlinear clearance problem of the electro-hydraulic servo system, a mathematical transfer model with clearance is established, and on this basis, a clearance compensation method based on the Hopfield neural network is proposed. In this way, clearance compensation can be realized by adjusting the parameters of neural network nodes, through simple and convenient operation. Finally, by setting different clearance values, the results of the step response and sine response curve before and after clearance compensation of the hydraulic system are compared, and the effectiveness of Hopfield neural network compensation clearance control is verified based on the comparison simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of attitude trajectory tracking of rigid bodies subject to external disturbances. The attitude control problem has been studied in the last decades and novel solutions have been proposed. Nevertheless, most of the proposed controllers only achieve local or almost global asymptotic stability without considering external disturbances. Contrary to other works, we focus on the problem of achieving almost global exponential stability of the attitude tracking errors in the presence of external disturbances using continuous control laws. We propose an attitude trajectory tracking controller based on the exponential coordinates of rotation in combination with a disturbance observer that estimates the exogenous signals. To solve this problem, we adopt a hierarchical approach, where the proposed control law is divided into a kinematic controller (outer control loop) and a velocity tracking controller (inner control loop). To design the disturbance observer, it is assumed that exogenous signals can be generated by a linear exosystem, i.e. the magnitude and phase of the disturbance are unknown. The almost global exponential stability of the closed-loop dynamics' equilibrium point was proved by a strict Lyapunov function. The performance of the proposed approach is assessed by numerical simulations and experimental tests on a low-cost quadrotor. [ABSTRACT FROM AUTHOR]

This paper is concerned with reset controller design and $ \mathcal {L}_2 $ L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and $ \mathcal {L}_2 $ L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the $ \mathcal {L}_2 $ L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

To reduce the communication and computation overhead of neural networks, a novel pinning event-triggered scheme (PETS) is developed in this paper, which enables pinning synchronization of uncertain coupled memristive neural networks (CMNNs) under limited resources. Time-varying delays, uncertainties, and mismatched parameters are all considered, which makes the system more interpretable. In addition, from the low energy cost point of view, an algorithm for pinned node selection is designed to further investigate the newly event-triggered function under limited communication resources. Meanwhile, based on the PETS and following the Lyapunov functional method, sufficient conditions for the pinning exponential stability of the proposed coupled error system are formulated, and the analysis of the self-triggered method shows that our method can efficiently avoid Zeno behavior under the newly determined triggered conditions, which contribute to better PETS performance. Extensive experiments demonstrate that the PETS significantly outperforms the existing schemes in terms of solution quality. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve combinatorial optimization problems by transforming the discrete optimization problem into a classical optimization problem over continuous circuit parameters. QAOA objective landscape is notorious for pervasive local minima, and its viability significantly relies on the efficacy of the classical optimizer. In this work, we design double adaptive-region Bayesian optimization (DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly outperforms conventional optimizers in terms of speed, accuracy, and stability. We also address the issues of measurement efficiency and the suppression of quantum noise by conducting the full optimization loop on a superconducting quantum processor as a proof of concept. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks. There is no universal way of optimizing the variation quantum circuits used in Noisy Intermediate-Scale Quantum (NISQ) applications. In this paper the authors introduce a new classical Bayesian optimizer, which converges much more quickly than conventional approaches, and test it for solving the Quantum Approximate Optimization Algorithm (QAOA) problem. [ABSTRACT FROM AUTHOR]

This paper studies the stability criterion and controller design for time-delay switched systems with input saturation. The main contributions of this paper are as follows: (1) Based on constructing the Lyapunov–Krasovskii functional (LKF) with the triple integral term and making full use of the delay lower bound information, the sufficient conditions for the exponential stability of the system are given. (2) A state feedback controller is designed for the input-saturated system. (3) The symmetric delay rate problem is considered to accurately define the derivative of LKF, which reduces the conservatism of the system. By reducing conservatism, that is, the time-delay upper bound is raised, allowing for a wider range of time-delay signals. Finally, the effectiveness of the proposed method is verified by the numerical examples. [ABSTRACT FROM AUTHOR]

Efficient integration of wind energy requires accurate wind power forecasting. This prediction is critical in optimising grid operation, energy trading, and effectively harnessing renewable resources. However, the wind's complex and variable nature poses considerable challenges to achieving accurate forecasts. In this context, the accuracy of wind parameter forecasts, including wind speed and direction, is essential to enhancing the precision of wind power predictions. The presence of missing data in these parameters further complicates the forecasting process. These missing values could result from sensor malfunctions, communication issues, or other technical constraints. Addressing this issue is essential to ensuring the reliability of wind power predictions and the stability of the power grid. This paper proposes a long short-term memory (LSTM) model to forecast missing wind speed and direction data to tackle these issues. A fractional-order neural network (FONN) with a fractional arctan activation function is also developed to enhance generated wind power prediction. The predictive efficacy of the FONN model is demonstrated through two comprehensive case studies. In the first case, wind direction and forecast wind speed data are used, while in the second case, wind speed and forecast wind direction data are used for predicting power. The proposed hybrid neural network model improves wind power forecasting accuracy and addresses data gaps. The model's performance is measured using mean errors and R2 values. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time annular domain stability and stabilisation for the positive systems. A new analysis method is proposed to obtain less conservative finite-time annular domain stability criteria and its superiority to modified Gronwall inequality is analysed. Moreover, conditions for the existence of state feedback and observer-based controllers that guarantee the closed-loop system to be positive and finite-time annular domain stable are given under the linear programming framework. Finally, two numerical examples are provided to show the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study a neural network-based fault-tolerant controller to improve the tracking control performance of an unmanned autonomous helicopter with system uncertainty, external disturbances and sensor faults, using the prescribed performance method. Design/methodology/approach: To ensure that the tracking error satisfies the prescribed performance, the authors adopt an error transformation function method. A control scheme based on the neural network and high-order disturbance observer is designed to guarantee the boundedness of the closed-loop system. A simulation is performed to prove the validity of the control scheme. Findings: The developed adaptive fault-tolerant control method makes the system with sensor fault realize tracking control. The error transformation function method can effectively handle the prescribed performance requirements. Sensor fault can be regarded as a type of system uncertainty. The uncertainty can be approximated accurately using neural networks. A high-order disturbance observer can effectively suppress compound disturbances. Originality/value: The tracking performance requirements of unmanned autonomous helicopter system are considered in the design of sensor fault-tolerant control. The inequality constraint that the output tracking error must satisfy is transformed into an unconstrained problem by introducing an error transformation function. The fault state of the velocity sensor is considered as the system uncertainty, and a neural network is used to approach the total uncertainty. Neural network estimation errors and external disturbances are treated as compound disturbances, and a high-order disturbance observer is constructed to compensate for them. [ABSTRACT FROM AUTHOR]

The current development of logic satisfiability in discrete Hopfield neural networks (DHNN)has been segregated into systematic logic and non-systematic logic. Most of the research tends to improve non-systematic logical rules to various extents, such as introducing the ratio of a negative literal and a flexible hybrid logical structure that combines systematic and non-systematic structures. However, the existing non-systematic logical rule exhibited a drawback concerning the impact of negative literal within the logical structure. Therefore, this paper presented a novel class of non-systematic logic called conditional random k satisfiability for k=1,2 while intentionally disregarding both positive literals in second-order clauses. The proposed logic was embedded into the discrete Hopfield neural network with the ultimate goal of minimizing the cost function. Moreover, a novel non-monotonic Smish activation function has been introduced with the aim of enhancing the quality of the final neuronal state. The performance of the proposed logic with new activation function was compared with other state of the art logical rules in conjunction with five different types of activation functions. Based on the findings, the proposed logic has obtained a lower learning error, with the highest total neuron variation TV=857 and lowest average of Jaccard index, JSI=0.5802. On top of that, the Smish activation function highlights its capability in the DHNN based on the result ratio of improvement Zm and TV. The ratio of improvement for Smish is consistently the highest throughout all the types of activation function, showing that Smish outperforms other types of activation functions in terms of Zm and TV. This new development of logical rule with the non-monotonic Smish activation function presents an alternative strategy to the logic mining technique. This finding will be of particular interest especially to the research areas of artificial neural network, logic satisfiability in DHNN and activation function. [ABSTRACT FROM AUTHOR]

In this paper, a new-type time-varying asymmetric integral barrier function is designed to handle the state constraint of nonlinear systems. The barrier Lyapunov function is developed by building an integral upper limit function with respect to transformation errors over an open set to cope with the position constraint of the robotic system. We know that the symmetric time-invariant constraint is only a particular situation of the asymmetric time-variant constraint, and thus compared to existing methods, it is capable of handling more general and broad practical engineering issues. We show that under the integral barrier Lyapunov function combining a disturbance observer-based tracking controller, the position vector tracks a desired trajectory successfully, while the constraint boundary is never violated. It can certify the exponential asymptotic stability of the robotic tracking system by using the given inequality relationship on barrier function and Lyapunov analysis. Finally, the feasibility of the presented algorithm is indicated by completing the simulations. [ABSTRACT FROM AUTHOR]

Sampled-data control of PDEs has become an active research area; however, existing results are confined to deterministic PDEs. Sampled-data controller design of stochastic PDEs is a challenging open problem. In this paper we suggest a solution to this problem for 1D stochastic diffusion-reaction equations under discrete-time nonlocal measurement via the modal decomposition method, where both the considered system and the measurement are subject to nonlinear multiplicative noise. We present two methods: a direct one with sampled-data controller implemented via zero-order hold device, and a dynamic-extension-based one with sampled-data controller implemented via a generalized hold device. For both methods, we provide mean-square L² exponential stability analysis of the full-order closed-loop system. We construct a Lyapunov functional V that depends on both the deterministic and stochastic parts of the finite-dimensional part of the closedloop system. We employ corresponding Ito's formulas for stochastic ODEs and PDEs, respectively, and further combine V with Halanay's inequality with respect to the expected value of V to compensate for sampling in the infinite-dimensional tail. We provide linear matrix inequalities (LMIs) for finding the observer dimension and upper bounds on sampling intervals and noise intensities that preserve the mean-square exponential stability. We prove that the LMIs are always feasible for large enough observer dimension and small enough bounds on sampling intervals and noise intensities. A numerical example demonstrates the efficiency of our methods. The example shows that for the same bounds on noise intensities, the dynamic-extension-based controller allows larger sampling intervals, but this is due to its complexity (generalized hold device for sample-data implementation compared to zero-order hold for the direct method). [ABSTRACT FROM AUTHOR]

This paper is dedicated to studying the mean square exponential stability of switched stochastic time‐varying delay neural networks with asynchronous switching aperiodic intermittent control. By utilizing the Halanay‐type inequality and designing appropriate asynchronous switching aperiodic intermittent control, several novel stability criteria of switched stochastic delay neural networks with asynchronous aperiodic intermittent control are presented under the Lyapunov function method and Lyapunov functional method. Among them, asynchronous switching aperiodic intermittent controllers are more practical and flexible compared to state feedback controllers. Finally, we provide two examples to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This note is to make some corrections on the assumptions in Theorems 1.2, 1.3, and 1.5 in our paper [Halil Ibrahim Kurt and Wenxian Shen, Journal of Differential Equations 355 (2023) 248–295]. [ABSTRACT FROM AUTHOR]

This paper investigates the coupled Patlak–Keller–Segel–Navier–Stokes (PKS–NS) system in two-dimensional bounded domains with a focus on global well-posedness and the formation of striking patterns, in which the boundary conditions are Neumann conditions for the cell density and the chemical concentration, and the Navier slip boundary condition with zero friction for the fluid velocity. We prove that the solution of the system exists globally in time in the case of subcritical mass. Concerning the critical mass case, we construct the boundary spot steady states rigorously via the inner-outer gluing method. While studying the global existence and the concentration phenomenon of the chemotaxis–fluid model, we develop the global W 2 , p theory for the 2D stationary Stokes system subject to Navier boundary conditions with zero friction and further establish semigroup estimates of the nonstationary counterpart by analyzing the Stokes eigenvalue problem. [ABSTRACT FROM AUTHOR]

In this paper, the state observer for coupled cyclic genetic regulatory networks with time delays is designed. The coupling network is composed of two cyclic genetic subnets, which inhibit each other directly. By constructing a suitable Lyapunov – Krasovskii functional velated to the eyclic struction, the delay-dependent stability criteria of the error system are investigated in the form of linear matrix inequalities. Thereby, the state observer of the considered genetic regulatory networks is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper examines a three-dimensional delayed discrete neural network model analytically and numerically to determine the existence of different types of bifurcations of the involved fixed points. The model exhibits different bifurcations such as pitchforks, flips, Neimark–Sackers, and flip-Neimark–Sackers. The critical coefficients are used to determine the structure of each bifurcation. The curves are calculated and plotted for each bifurcation when the parameters are changed. Further, these bifurcations are theoretically analyzed and numerically verified. From the obtained results, we observed that by drawing the curves associated with each bifurcation, the numerical simulations are consistent with the analytical results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the existence, uniqueness and stability of solutions for some nonlocal impulsive evolution problems involving conformable fractional derivative. The main results are based on fixed point theorems combined with the semigroup theory. As applications, we give an example to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays. First, the model of fractional-order inertial memristive neural network with time-varying delays is proposed, which is more universal and less conservative than the integer-order inertial memristive neural network with time-varying delays. Second, one lemma about the compound property of Caputo fractional derivative and integral is given. According to the compound property of Caputo fractional derivative and appropriate variable substitution, the original inertial memristive system translates a routine inertial memristive system. And, using the Filippov discontinuous theory, Lyapunov stability theory, and Mittag-Leffler convergence, several sufficient conditions are derived to ensure the global Mittag-Leffler synchronization of Caputo fractional-order inertial memristive neural networks. An effective feedback controller is proposed for fractional-order inertial memristive neural networks with time-varying delays, such that the global Mittag-Leffler synchronization between the slave system and the master system can be achieved. Finally, a simulation example is given to verify the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

The coupling between neurons can lead to diverse neural network architectures, with the Hopfield neural network (HNN) being particularly noteworthy for its resemblance to human brain function and its potential in modeling chaotic systems. This paper introduces a novel approach: a fractional-order HNN coupled with a hyperbolic tangent-type memristor. Initially, we propose a new model for the hyperbolic tangent-type memristor and fingerprints. Subsequently, we construct a memristor-coupled fractional-order Hopfield neural network (mFOHNN) and explore its dynamic behavior using various analytical tools, including phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, Poincaré maps, and attractor basins. Our findings reveal rich coexisting bifurcation behavior in the neural network model, influenced by different initial values of coexisting attractors. Finally, we validate the model through analysis and implementation using Multisim circuit simulation software and FPGA hardware, respectively. [ABSTRACT FROM AUTHOR]

We study a free boundary problem on the evolution of a radial tumor with triple-layered structure. Based on the nutrient thresholds $ \sigma_Q $ and $ \sigma_D $, cells in the tumor spheroid are divided into three types, i.e. proliferating cells, quiescent cells and necrotic cells, hence it forms a layered structure from tumor's surface to its center. The novelty of this paper is that the growth of the triple-layered tumor is first taken into rigorous analysis, and the difficulty arises from the two unknown moving interfaces $ \eta $ and $ \rho $ between different cell layers inside the tumor. We show existence and uniqueness of the stationary solution to the system for different external nutrient supply $ \bar \sigma $. It is proved that there exist two constants $ \sigma^* $ and $ \sigma_* $ with the relation $ \sigma^*> \sigma_*>\tilde \sigma $, such that if $ \bar \sigma> \sigma^* $, the dormant tumor forms a triple-layered structure; if $ \sigma_*<\bar \sigma \le \sigma^* $, the dormant tumor has double layers with proliferating cells and quiescent cells; if $ \tilde \sigma <\bar \sigma\le \sigma_* $, the dormant tumor is filled with only proliferating cells and appears as a single layer; and if $ \bar \sigma\le\tilde \sigma $, the dormant tumor vanishes. The asymptotic stability of the stationary solution above is also studied. We can show the tendency of the evolutionary tumor towards its dormant state by using only $ \bar \sigma $ and the initial radius $ R_0 $ as well. [ABSTRACT FROM AUTHOR]

This study develops a "Skill Talent Ecological Evaluation Model" across cultivation, potential energy, kinetic energy, innovation, and service and support ecologies. AHP-entropy determines indicator weights, Hopfield neural network assesses talent ecology levels, and the PVAR model analyzes digital transformation effects. Findings reveal: Cultivation ecology rates A, potential ecology rates B+, kinetic ecology rates B-, service and support ecology rates B-, and innovation ecology rates C. Digital transformation spurs skill demand, impacting talent and economic contributions. Kinetic ecology sees increased demand, potentially impacting traditional industries positively. Innovation ecology necessitates continuous skill learning. Service and support ecology witnesses growth in digital entrepreneurship, requiring policy incentives and incubation center support. [ABSTRACT FROM AUTHOR]

In modern power systems, the uncertainty and volatility of generation and loads greatly increase the balance discrepancy between the power supply and demand, creating major potential security hazards. To limit out‐of‐bound frequencies, an effective frequency control method for power systems with interval uncertain disturbances is proposed. Based on the state space model of the system frequency response with delays, linear matrix inequalities are constructed based on the input‒output finite‐time stability of the system frequency. By searching for the output feedback gain and altering the time delay with the Padé approximation, the feasibility of the linear matrix inequalities is improved, and a frequency controller is designed. The simulation results show that the proposed method can effectively control frequency deviations. When the closed‐loop system is disturbed by uncertain power fluctuations, its frequency will always remain within the allowable range to ensure the secure operation of the power system. [ABSTRACT FROM AUTHOR]

The concept of perfect equilibrium, formulated by Selten (Int J Game Theory 4:25–55, 1975), serves as an effective characterization of rationality in strategy perturbation. In our study, we propose a modified version of perfect equilibrium that incorporates perturbation control parameters. To match the beliefs with the equilibrium choice probabilities, the logistic quantal response equilibrium (logistic QRE) was established by McKelvey and Palfrey (Games Econ Behav 10:6–38, 1995), which is only able to select a Nash equilibrium. By introducing a linear combination between a mixed strategy profile and a given vector with positive elements, this paper develops a variant of the logistic QRE for the selection of the special version of perfect equilibrium. Expanding upon this variant, we construct an equilibrium system that incorporates an exponential function of an extra variable. Through rigorous error-bound analysis, we demonstrate that the solution set of this equilibrium system leads to a perfect equilibrium as the extra variable approaches zero. Consequently, we establish the existence of a smooth path to a perfect equilibrium and employ an exponential transformation of variables to ensure numerical stability. To make a numerical comparison, we capitalize on a variant of the square-root QRE, which yields another smooth path to a perfect equilibrium. Numerical results further verify the effectiveness and efficiency of the proposed differentiable path-following methods. [ABSTRACT FROM AUTHOR]

This paper analyzes the problem of simultaneous fault detection and control of the six-rotor unmanned aerial vehicle control system, considering external disturbance, measurement disturbance, and actuator fault. The integral event trigger mechanism is introduced in the control side and sensor side of the system. Based on Lyapunov stability and H∞ control theory, the sufficient conditions to make the fault system asymptotically stable and have certain performance indexes are given by means of linear matrix inequalities; at the same time, the design criteria of event trigger parameters are also given. The linear matrix inequality is decoupled, and the calculation method of gain matrix of simultaneous fault detection and control module is given. The effectiveness of the proposed method is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-triggered control of switched two-dimensional (2D) continuous-discrete systems in Roesser model. A more general event-triggered scheme is proposed to reduce unnecessary resource waste and data redundancy, where a weighing coefficient and multiple parameter matrices are used. Based on the proposed event-triggered mechanism, a state feedback controller and a state-dependent switching signal are proposed. By using the multiple Lyapunov function method, sufficient conditions for the exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, two examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

There exist numerous multi‐path signals with impulsive noise (IN) in a multi‐path propagation environment. The direction‐of‐arrival (DOA) is highly challenging to be assessed because of the strong IN. For various military along with civilian applications, DOA estimation has turned into a hopeful technology. But, estimating DOA for multipath signals with IN environments is extremely complicated. A desirable output is not attained by several existent techniques, namely subspace‐centric approaches, maximum likelihood techniques, along with sparse representation‐centric methods, for DOA assessment. Therefore, an effective satin bowerbird optimization‐based deep learning neural network centered DOA estimation upon single snapshots is proposed in this paper for attaining robust and precise DOA estimation in multipath and IN environments. An arbitrary array configuration is employed by utilizing the proposed work as an input signal for establishing the received signal's model. Pre‐processing, time‐frequency domain conversion, feature extraction, feature reduction and DOA estimation are the proposed method's 5 disparate stages. To evince the proposed model's efficacy, its outcomes are analogized with other prevailing techniques regarding some performance metrics. The proposed model attains the root mean square error of 0.6484366‐AZ and 0.6484366‐EA, root mean squared percentage error (RMPSE) of 4.636107‐AZ and 5.628599‐EA and probability of resolution of 0.967999‐AZ and 0.962841‐EA, which are extremely less when compared to the prevailing methods; thus, depicting the superiority of the proposed model for an effective DOA estimation. [ABSTRACT FROM AUTHOR]

In the realm of modeling biological systems with memory, particularly those involving intricate interactions like tumor-immune responses, the utilization of multiple time delays and Caputo-type fractional-order derivatives represents a cutting-edge approach. In this research paper, we introduce a novel fractional-order model to investigate the dynamic interplay between tumors and macrophages, a key component of the immune system, while incorporating multiple time delays into our framework. Our proposed model comprises a system of three Caputo-type fractional-order differential equations, each representing distinct cell populations: tumor cells, anti-tumor cells (specifically M1-type macrophages with pro-inflammatory properties), and pro-tumor cells (M2-type macrophages with immune-suppressive characteristics). The stability of equilibria is discussed by analyzing the characteristic equations for each case, and the existence conditions for the Hopf bifurcation are obtained according to the critical values of delay parameters. Furthermore, numerical simulations are presented in order to verify the analytical results obtained for stability and Hopf-bifurcation with respect to the two-time delay parameters τ1 and τ2. The analysis shows the rich dynamics of the model according to the fractional-order parameter and the time delay parameters. [ABSTRACT FROM AUTHOR]