This paper develops an optimal leader-following consensus protocol for a second-order nonlinear multi-agent system with disturbance via dynamic event-triggered sliding mode strategy. The proposed control protocol contains two dynamic event-triggered mechanisms, which are used to regulate the updates of the discontinuous control and optimal consensus control parts. Considering the effect of disturbance, a novel distributed event-triggered sliding mode control protocol is developed to ensure the predefined-time reachability of the sliding surface and yields sliding mode dynamics that are robust to external disturbances. To further obtain the optimal event-triggered consensus protocol, an online critic neural network is designed with weight updated by the concurrent learning method. Then, the asymptotic stability of sliding mode dynamics and uniform ultimate boundedness of the weight estimation errors are proved based on the Lyapunov method. Finally, the effectiveness of the proposed method is verified by simulations of multiquadrotor unmanned aerial vehicle models.

This article proposes a distributed Lagrange alternating gradient descent (LAGD) algorithm with a fixed step size for constrained optimization over a multiagent communication network. Interconnected by multiagent networks, agents optimize their own objective function subject to local constraints cooperatively, and the whole network shares globally coupled constraints. All agents reach consensus on the estimations of multipliers via the network communication to handle the globally coupled constraints, and the decision variable vectors converge to the optimal solution along the Lagrange gradient direction. The convergence of the algorithm is proven under the condition of fixed step sizes subject to a theoretical upper bound. An economic dispatch problem in a power system and a numerical example are elaborated to verify and demonstrate the effectiveness of the algorithm.

This article addresses the optimal state observation and leader-following consensus for a nonlinear multiagent system (MAS) with input saturation under the Stackelberg game framework. The dynamics and states of followers are unknown, the leader's dynamics is unknown, and the leader's state is accessible only to a subset of followers. First, a distributed estimation algorithm is developed for each follower to estimate the leader's state. Then, a game-based observer is designed to estimate the follower state, where the bidirectional interaction between the observer and follower dynamics is considered. The follower dynamics and observer are modeled as leader and follower players in the Stackelberg game, respectively. Based on the proposed structure, an optimal auxiliary controller for the observer and an optimal consensus controller are developed. Furthermore, a fuzzy reinforcement learning approach approximates the unknown dynamics and derives the optimal state observers and leader-following consensus controllers. All closed-loop signals are guaranteed to be uniformly ultimately bounded based on the Lyapunov method. Finally, simulations are provided to validate the effectiveness of the proposed approach.

This paper studies the distributed optimal strategy problem in multi-agent pursuit-evasion game for capture and formation control under false data injection attacks (FDIAs) and input saturation constraints. In the game, pursuers aim to approach evaders while evaders attempt to keep a distance, and agents within the same team are required to preserve cohesion. To achieve control objectives under the FDIAs and input saturation constraints, a hierarchical control framework is developed, which includes a sliding mode control (SMC) layer and an optimal control layer. Moreover, the SMC strategy is designed to mitigate the effects of FDIAs and input saturation. Then, since the sliding mode dynamics involves coupling terms associated with formation displacement, a fuzzy reinforcement learningbased optimal control strategy is proposed to achieve capture and formation aims. Furthermore, based on the Lyapunov method, it is proven that all closed-loop signals are uniformly ultimately bounded. Finally, the effectiveness of the proposed method is validated by simulations conducted on distributed mobile robots.

Point cloud is complex 3D data characterized by its irregularity and unordered structure. In contrast to previous efforts aimed at extracting local geometric information by sophisticated techniques, we delve into the rich topological information of point clouds using persistent homology. First, we introduce two vectorization methods, PPDTF and PDTF, to transform topological information into a format suitable for deep neural networks. Then we propose TopoLayer, a simple but effective and universal neural network layer seamlessly integrated into existing architectures. Integration of TopoLayer, without architectural modifications, significantly improves established models such as PointMLP and PointNet++. For classification on ModelNet40, the class mean accuracy of PointMLP notably improves from 91.3% to 91.8%, surpassing the state-of-the-art PointMixer. Additionally, PointNet++ achieves a remarkable gain of 2.7%. For part segmentation on ShapeNetPart, PointMLP achieves a new state-of-the-art performance with 85.1% Cls.mIoU, while PointNet++ secures a significant 0.9% increase. The code is available at https://github.com/Zechao-Guan/TopoLayer.

This article studies the secure leader-follower consensus of nonlinear multiagent systems under multimode Denial-of-Service attacks. According to the topology characteristics after attacks, three kinds of different attack modes are introduced. Moreover, the common zero-topology attack is encompassed within the multimode attacks considered in this article. Due to the difficulty of directly obtaining the state of the system in some circumstances, a state observer is designed utilizing localized output information of the MASs to estimate the state. By applying suitable observer-based controller and Lyapunov method, some sufficient conditions are presented to ensure the observer-based secure consensus of the MASs under multimode DoS attacks. Furthermore, the obtained results can be extended to linear MASs under DoS attacks. Finally, two practical examples on power system are provided to demonstrate the validity of the derived theoretical results.

This article introduces an innovative distributed algorithm tailored for achieving predefined-time convergence in addressing time-varying resource allocation problem under directed networks. The attainment of predefined-time convergence is crucial for fulfilling real-time requirements, ensuring quality and safety standards, and optimizing the efficiency of resource utilization. It grants users the flexibility to tailor the convergence time according to their specific requirements and constraints. Moreover, the algorithm integrates an auxiliary system to ensure continual satisfaction of the global equality constraint. A distinctive feature lies in the utilization of nonhomogeneous functions with exponential terms, facilitating the achievement of predefined-time convergence. Compared to some existing algorithms with dynamic behaviors, including asymptotical convergence, exponential convergence, and fixed-time convergence, the proposed algorithm demonstrates superior convergence speed. Finally, we demonstrate the effectiveness of the designed technique through numerical simulations, comparisons with state-of-the-art algorithms, and its application to multienergy management problem in the multimicrogrid system.

This article investigates the secure leader–following consensus of multiagent systems with unknown follower dynamics under two types of denial-of-service attacks: connectivity-maintained and connectivity-broken attacks. A predefined-time resilient distributed observer to achieve predefined-time observation of the leader's state is constructed by incorporating a time-varying piecewise function with an online update at the initial instant. During the connectivity-maintained intervals, all agents can achieve predefined-time observation of the leader. During the connectivity-broken intervals, agents that have direct or indirect access to the leader's state can still accomplish the predefined-time observation. Since the leader state observation cannot be ensured for all agents during the connectivity-broken intervals, a new persistent dwell-time switching model is introduced to describe the switching between the two types of attacks, and novel sufficient conditions are derived to ensure that all agents can observe the leader's state based on multiple Lyapunov function approach. Furthermore, a predefined-time sliding mode controller combining the resilient distributed observer and fuzzy reinforcement learning strategy is proposed to ensure leader–following consensus. Finally, the effectiveness of the proposed method is validated through simulations and comparisons using a distributed multiple robot arm system.

This article proposes a unified consensus algorithm with predefined-time convergence aimed at solving time-varying optimization problems based on multiagent systems under connected and undirected networks. The goal is to minimize the sum of local objective functions in a predefined time, where each agent possesses knowledge only of its local objective function. Two problems are addressed in this article: 1) optimal consensus and 2) optimal resource allocation, in which both the local objective function and the coupled equality constraint vary with time. The proposed unified consensus algorithm achieves the predefined-time optimization by leveraging the predefined-time stability theory under mild assumptions. Specifically, by transforming into the Lagrange dual problem, the optimal resource allocation problem is solved by the unified consensus algorithm from the perspective of dual variables. It is worth mentioning that the proposed unified consensus algorithm does not rely on the second-order information of objective functions, including the partial derivative of the gradient concerning time and the Hessian information. Finally, two simulation examples compared with state-of-the-art methods, application to the large-scale system, and application to the target encirclement problem of multirobot systems are provided to substantiate the theoretical results.

In this article, an unified distributed multiagent system is proposed to minimize the time-varying quadratic function under the time-varying coupled equality constraint, which is further applied to target encirclement of the multirobot system. The time-varying quadratic programming problem under consideration is a generalized version of some found in the literature. The proposed unified distributed multiagent system is effective in both of the following cases of time-varying quadratic programming: one with the nonidentical time-invariant Hessian and constraint matrices, and the other with the identical time-varying Hessian and constraint matrices. The convergence of the time-varying states can be guaranteed if the graph of the communication network is connected and undirected, subject to certain mild conditions. Additionally, simulations show that the suggested approach is effective in resolving the target encirclement problem of the multirobot systems.

Recently, deep learning has been widely used in the classification of EEG signals and achieved satisfactory results. However, the correlation between EEG electrodes is rarely considered, which has been proved that there are indeed connections between different brain regions. After considering the connections between EEG electrodes, the graph convolutional neural network is applied to detect human motor intents from EEG signals, where EEG data are transformed into graph data through phase lag index, time-domain and frequency-domain features with different signal bands. Meanwhile, a multi-scale attention mechanism is proposed to the network to improve the accuracy of classification. By using the multi-scale attention-based graph convolutional neural network, the accuracy of 93.22% is achieved with 10-fold cross-validation, which is higher than the compared methods which ignore the spatial correlations of EEG signals.

This article mainly investigates how to reduce the communication cost in multiagent system (MAS) for distributed optimization. First, a continuous-time distributed optimization model based on MAS is proposed for resource allocation (RA) with periodic communication. All agents in the system do not need to be in constant contact with their neighbors, but contact at set intervals. This will greatly reduce the communication consumption of the system. Second, to further reduce the communication cost, MAS with event-triggered communication is proposed based on periodic communication. It is proved that the system is convergent to an optimal solution of the investigated problem subject to bound and equality constraints. Finally, two examples with simulations are given to verify the performance of the proposed system.

In this article, a discrete-time distributed optimization algorithm is proposed for solving the economic dispatch (ED) problem with some groups of generator units to communicate over a connected graph, which is independent of the power system. The ED problem is converted to a distributed optimization problem with an objective of the sum of individual convex functions and constraints of local generators. Based on the optimal conditions, a class of distributed algorithms is designed to find the solution to the ED problem. The distributed algorithm can be realized as a multiagent system with a connected graph, whose convergence can be proved using the dynamic analysis method. Moreover, experiments with simulations are presented to demonstrate the performance of the proposed algorithm.

In this article, we revisit the problem of distributed neuroadaptive consensus for uncertain multiagent systems (MASs) in the presence of unmodeled nonlinearities as well as unknown disturbances. Robust consensus controllers comprising a linear feedback term, a discontinuous feedback term, and a neural network approximation term are constructed, where in each term, the weight part is endowed with some dynamical changing law. The asymptotic convergence of the consensus errors is theoretically proved based on the graph theory, nonsmooth analysis, and Barbalat's lemma. Both leaderless consensus and leader-follower tracking problems are considered before the results are further extended to containment problem in the presence of multileaders. A dramatic feature of the proposed method, in comparison with related works, is the fully distributed fashion of the information, requiring neither the underlying Laplacian eigenvalues nor the input upper bounds of the leaders (if exist). Several numerical examples are presented to testify the theoretical results.

In this paper, the optimization of the finite-time consensus of a multiagent system is studied when the leader is disturbed by white noise. Different from the consensus problem itself, this paper is devoted to optimizing the performance of the consensus and the constructive method and martingale method are used to guarantee the effectiveness of the optimization. Another contribution is that the problem of the optimal control with the piecewise constant controller gains under a stochastic environment is solved, and the reformed dynamic principle and the reformed Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs) are proposed by using the splitting method and Feynman–Kac formula. Furthermore, since the multiagent system often runs on a high-dimensional space, a heuristic method is proposed based on the derivation of the reformed HJB PDEs and the scalar of the computational complexity of the PDEs is equivalent to that of a system of ordinary differential equations with the same dimensions when the multiagent system can be described as a piecewise linear system. Finally, the heuristic method is compared with usual filtering methods for solving engineering problems by a numerical example and it is found that the heuristic method achieves higher precision in finite time.

In this paper, a continuous-time multiagent system is proposed for solving optimal resource allocation problems with local allocation feasible constraints. In the system, all the primal agents are divided into different groups. We use dual variables which describe the dual agents to represent the groups of the original agents. The groups of dual agents are used to communicate with others on behalf of the primal agents to reduce communication costs. That is to say, primal agents aim to seek their own optimal solutions by using local information. And dual agents represent primal agents to communicate with other agents in different groups by using the whole group information. The two kinds of agents cooperate to find the optimal solution of the problem. In this way, we only need to know the connections of dual agents to design the multiagent network, and do not need to consider the connections of the primal agents. So the communication cost and the amount of variables will be largely reduced especially for large-scale problem. Furthermore, it is proved that the multiagent system can reach consensus with respect to the dual variables. At the same time, the primal variables are convergent to the optimal solutions of the optimization problem under some certain assumptions on the communication network. For large-scale problem if we take the groups as areas, then the system is suitable for multiarea problem. Simulation results are presented to demonstrate the performance of the proposed multiagent system.

In this paper, a composite prescribed performance control strategy is developed for stabilizing dc/dc boost converter feeding constant power loads. First, by employing the exact feedback linearization technique, the nonlinear uncertain dc converter system is first transformed into the Brunovsky’s canonical form. Then, a nonlinear disturbance observer is utilized to evaluate the dynamic change of load power and the accuracy of output voltage regulated by feedforward compensation. Next, the prescribed performance controller is elaborately designed to ensure that the tracking error of output voltage is always within the margin of predefined error bounds. Based on the backstepping design approach, the composite nonlinear controller with prescribed performance is determined. Finally, the numerical simulation results are presented to demonstrate the tracking performance of the proposed controller.

This paper deals with sparse signal reconstruction by designing a discrete-time projection neural network. Sparse signal reconstruction can be converted into an$L_{1}$-minimization problem, which can also be changed into the unconstrained basis pursuit denoising problem. To solve the$L_{1}$-minimization problem, an iterative algorithm is proposed based on the discrete-time projection neural network, and the global convergence of the algorithm is analyzed by using Lyapunov method. Experiments on sparse signal reconstruction and several popular face data sets are organized to illustrate the effectiveness and performance of the proposed algorithm. The experimental results show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Moreover, the value of the step size of the proposed algorithm is close to 1/2, thus a fast convergence rate is potentially possible. Furthermore, the proposed algorithm achieves better classification performance compared with some other algorithms for face recognition.

This paper is concerned with multiple-objective distributed optimization. Based on objective weighting and decision space decomposition, a collaborative neurodynamic approach to multiobjective distributed optimization is presented. In the approach, a system of collaborative neural networks is developed to search for Pareto optimal solutions, where each neural network is associated with one objective function and given constraints. Sufficient conditions are derived for ascertaining the convergence to a Pareto optimal solution of the collaborative neurodynamic system. In addition, it is proved that each connected subsystem can generate a Pareto optimal solution when the communication topology is disconnected. Then, a switching-topology-based method is proposed to compute multiple Pareto optimal solutions for discretized approximation of Pareto front. Finally, simulation results are discussed to substantiate the performance of the collaborative neurodynamic approach. A portfolio selection application is also given.

In this paper, a continuous-time distributed optimization algorithm based on multi-agent system is proposed for solving the distributed least absolute deviation problems subject to hybrid constraints. In the multi-agent network, each of the L1-norm functions is realized using the projection operator. Meanwhile, each agent must be subject to the local hybrid constraints. Then all the agents constitute a network with connected graph to cooperate to seek the optimal solutions with consensus. The performance of the proposed distributed algorithm is illustrated using a numerical example with simulations.

This paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks (RNNs) for distributed constrained optimization. The objective function of the distributed optimization problems to be solved is a sum of local convex objective functions, which may be nonsmooth. Subject to its local constraints, each local objective function is minimized individually by using an RNN, with consensus among others. In contrast to existing continuous-time distributed optimization methods, the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems. Simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach. In addition, an application to the optimal placement problem is delineated to demonstrate the viability of the approach.

In this paper, distributed optimization is addressed based on a continuous-time multiagent system in the presence of time-varying communication delays. First, the relationship between optimal solutions and the equilibrium points of the multiagent system with time delay is revealed. Next, delay-dependent and delay-independent sufficient conditions in form of linear matrix inequality are derived for ascertaining convergence to optimal solutions, in the cases of slow-varying delay and fast-varying delay. Furthermore, a set of conditions are also obtained for the delay-free case. In addition, a sampled-data communication scheme is presented based on the conditions for the fast varying delay systems. Simulation results are presented to substantiate the theoretical results. An application for distributed parameter estimation is also given.

This paper presents several L1-minimization algorithms for sparse signal reconstruction based on a continuous-time projection neural network (PNN). First, a one-layer projection neural network is designed based on a projection operator and a projection matrix. The stability and global convergence of the proposed neural network are proved. Then, based on a discrete-time version of the PNN, several L1-minimization algorithms for sparse signal reconstruction are developed and analyzed. Experimental results based on random Gaussian sparse signals show the effectiveness and performance of the proposed algorithms. Moreover, experimental results based on two face image databases are presented that reveal the influence of sparsity to the recognition rate. The algorithms are shown to be robust to the amplitude and sparsity level of signals as well as efficient with high convergence rate compared with several existing L1-minimization algorithms.

This paper presents a continuous-time multi-agent network for distributed least absolute deviation (DLAD). The objective function of the DLAD problem is a sum of many least absolute deviation functions. In the multi-agent network, each agent connects with its neighbors locally and they cooperate to obtain the optimal solutions with consensus. The proposed multi-agent network is in fact a collective system with each agent being considered as a recurrent neural network. Simulation results on a numerical example are presented to illustrate the effectiveness and characteristics of the proposed distributed optimization method.

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

This paper presents one-layer projection neural networks based on projection operators for solving constrained variational inequalities and related optimization problems. Sufficient conditions for global convergence of the proposed neural networks are provided based on Lyapunov stability. Compared with the existing neural networks for variational inequalities and optimization, the proposed neural networks have lower model complexities. In addition, some improved criteria for global convergence are given. Compared with our previous work, a design parameter has been added in the projection neural network models, and it results in some improved performance. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural networks.

This paper presents a continuous-time recurrent neural network described by differential equations for realtime support vector regression (SVR). The SVR is first formulated as a convex quadratic programming problem, and then a continuous-time recurrent neural network with one-layer structure is designed for training the support vector machine. Furthermore, simulation results on an illustrative example are given to demonstrate the effectiveness and performance of the proposed neural network.

This paper presents a decision-making model described by a recurrent neural network for dynamic portfolio optimization. The portfolio-optimization problem is first converted into a constrained fractional programming problem. Since the objective function in the programming problem is not convex, the traditional optimization techniques are no longer applicable for solving this problem. Fortunately, the objective function in the fractional programming is pseudoconvex on the feasible region. It leads to a one-layer recurrent neural network modeled by means of a discontinuous dynamic system. To ensure the optimal solutions for portfolio optimization, the convergence of the proposed neural network is analyzed and proved. In fact, the neural network guarantees to get the optimal solutions for portfolio-investment advice if some mild conditions are satisfied. A numerical example with simulation results substantiates the effectiveness and illustrates the characteristics of the proposed neural network.

This paper presents a one-layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints. The proposed neural network is designed based on two projection operators: linear equality constraints, and bound constraints. The objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex (pseudoconvex) on a set defined by the constraints. Compared with existing recurrent neural networks for nonsmooth optimization, the proposed model does not have any design parameter, which is more convenient for design and implementation. It is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex. Simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

In this paper, a one-layer recurrent neural network is presented for solving single-ration linear fractional programming problems subject to linear equality and box bound constraints. The convergence condition is derived to guarantee the solution optimality to the fractional programming problems if the design parameters in the neural network are larger than the derived lower bounds. Two numerical examples with simulation results show that the proposed neural network is efficient and accurate for solving constrained linear fractional programming problems.

In this paper, a one-layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints. The global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex. The finite-time state convergence to the feasible region defined by the equality constraints is also proved. In addition, global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region. Simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network.

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

In this paper, a one-layer recurrent neural network is proposed for solving nonconvex optimization problems subject to general inequality constraints, designed based on an exact penalty function method. It is proved herein that any neuron state of the proposed neural network is convergent to the feasible region in finite time and stays there thereafter, provided that the penalty parameter is sufficiently large. The lower bounds of the penalty parameter and convergence time are also estimated. In addition, any neural state of the proposed neural network is convergent to its equilibrium point set which satisfies the Karush-Kuhn-Tucker conditions of the optimization problem. Moreover, the equilibrium point set is equivalent to the optimal solution to the nonconvex optimization problem if the objective function and constraints satisfy given conditions. Four numerical examples are provided to illustrate the performances of the proposed neural network.

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

In this paper, based on a one-neuron recurrent neural network, a novel k-winners-take-all ( k -WTA) network is proposed. Finite time convergence of the proposed neural network is proved using the Lyapunov method. The k-WTA operation is first converted equivalently into a linear programming problem. Then, a one-neuron recurrent neural network is proposed to get the kth or (k+1)th largest inputs of the k-WTA problem. Furthermore, a k-WTA network is designed based on the proposed neural network to perform the k-WTA operation. Compared with the existing k-WTA networks, the proposed network has simple structure and finite time convergence. In addition, simulation results on numerical examples show the effectiveness and performance of the proposed k-WTA network.

Based on the projection operator, a recurrent neural network is proposed for solving extended general variational inequalities (EGVIs). Sufficient conditions are provided to ensure the global convergence of the proposed neural network based on Lyapunov methods. Compared with the existing neural networks for variational inequalities, the proposed neural network is a modified version of the general projection neural network existing in the literature and capable of solving the EGVI problems. In addition, simulation results on numerical examples show the effectiveness and performance of the proposed neural network.

This paper presents a one-layer recurrent neural network for solving convex programming problems subject to linear equality and nonnegativity constraints. The number of neurons in the neural network is equal to that of decision variables in the optimization problem. Compared with the existing neural networks for optimization, the proposed neural network has lower model complexity. Moreover, the proposed neural network is proved to be globally convergent to the optimal solution(s) under some mild conditions. Simulation results show the effectiveness and performance of the proposed neural network.

A one-layer recurrent neural network with a discontinuous activation function is proposed for linear programming. The number of neurons in the neural network is equal to that of decision variables in the linear programming problem. It is proven that the neural network with a sufficiently high gain is globally convergent to the optimal solution. Its application to linear assignment is discussed to demonstrate the utility of the neural network. Several simulation examples are given to show the effectiveness and characteristics of the neural network.

In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.

This paper presents a one-layer recurrent neural network with a unipolar hard-limiting activation function for k-winners-take-all (kWTA) operation. The kWTA operation is first converted into an equivalent quadratic programming problem. Then a one-layer recurrent neural network is constructed. The neural network is guaranteed to be capable of performing the kWTA operation in real time. The stability and convergence of the neural network are proven by using Lyapunov and nonsmooth analysis methods.

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.