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This paper investigates the exponential bipartite synchronization of a general class of delayed signed networks with multi-links by using an aperiodically intermittent control strategy. The main result is a set of sufficient conditions for bipartite synchronization that depend on the network's topology, control gain, and the maximum proportion of rest time. An application to Chua's circuits is then considered, and some numerical simulation results are presented. [ABSTRACT FROM AUTHOR]

In this paper, a smoothing approximation-based adaptive neurodynamic approach is proposed for a nonsmooth resource allocation problem (NRAP) with multiple constraints. The smoothing approximation method is combined with multi-agent systems to avoid the introduction of set-valued subgradient terms, thereby facilitating the practical implementation of the neurodynamic approach. In addition, using the adaptive penalty technique, private inequality constraints are processed, which eliminates the need for additional quantitative estimation of penalty parameters and significantly reduces the computational cost. Moreover, to reduce the impact of smoothing approximation on the convergence of the neurodynamic approach, time-varying control parameters are introduced. Due to the parallel computing characteristics of multi-agent systems, the neurodynamic approach proposed in this paper is completely distributed. Theoretical proof shows that the state solution of the neurodynamic approach converges to the optimal solution of NRAP. Finally, two application examples are used to validate the feasibility of the neurodynamic approach. [ABSTRACT FROM AUTHOR]

This paper aims to study the Nash equilibrium (NE) seeking algorithm of noncooperative game with second-order system under strongly connected digraph. In the algorithm, velocity information is not directly accessible to players, in order to avoid the need for additional velocity observers. Meanwhile, for position information, the position estimation of all the other players under local communication is completed in fixed time. To address the aforementioned concern, a NE seeking algorithm with a two-time-scale structure is designed. (1) For reduced system, a second-order velocity estimation model based on state observer is introduced to avoid direct acquisition of velocity information; (2) For fast compensation mechanism, each player uses leader-following consensus protocol to estimate the position of all the other players. The fixed-time consensus protocol is utilized to ensure that the position is estimated in fixed time. Then, aiming to reduce the communication costs and communication burden among players, the event-triggered mechanism is introduced into the above algorithm, and Zeno behavior is excluded. Lastly, a self-organized network problem involving autonomous vehicles is presented to validate the efficacy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a novel distributed adaptive neurodynamic approach (DANA) based on proportional integral technique is proposed to solve distributed optimization problem on multi-agent systems. The goal is that all agents reach consensus in finite time and converge to the optimal solution of the global objective function in fixed time. In the proposed approach, the proportional technique drives all agents to reach consensus, and the integral technique is used to offset the influence of the gradient term of the objective function. On the other hand, in order to avoid the prior estimation of gain parameter and the global gradient information, as the main contribution of this paper, the adaptive idea is considered into proportional integral technique. The results show that the adaptive integral technique can automatically adjust the gain according to the maximum consensus error between agents, so as to ensure that agents can achieve consensus in finite time. Then the theoretical results are applied to voltage distribution and logistic regression. Numerical simulation verifies the effectiveness of DANA. [ABSTRACT FROM AUTHOR]

As artificial intelligence and large data develop, distributed optimization shows the great potential in the research of machine learning, particularly deep learning. As an important distributed optimization problem, the nonsmooth distributed optimization problem over an undirected multi-agent system with inequality and equality constraints frequently appears in deep learning. To deal with this optimization problem cooperatively, a novel neural network with lower dimension of solution space is presented. It is demonstrated that the state solution of proposed approach can enter the feasible region. Also, it can also prove that the state solution achieves consensus and finally converges to the optimal solution set. Moreover, the proposed approach here does not depend on the boundedness of the feasible region, which is a necessary assumption in some simplified neural network. Finally, some simulation results and a practical application are given to reveal the efficacy and practicability. [ABSTRACT FROM AUTHOR]

Bi-objective optimization problems occur widely in engineering and science. This paper considers lexicographic method solution of the bi-objective optimization problems, feedback neural networks are adopted as optimization tools. The two objectives are sorted according to their priority, and then the bi-objective optimization problem is converted to two optimization problems with single-objective, namely, the high-priority optimization problem and the low-priority optimization problem. First, a classical neural network is applied for the high-priority optimization problem. Then, a novel feedback neural network is constructed to find an optimal solution of the low-priority optimization problem in the optimal solution set of the high-priority optimization problem. It is proved that any accumulation point of the state sequence of the proposed feedback neural network is a Pareto optimal solution to the considered bi-objective optimization problem. In contrast with the existing neural networks, the proposed neural network has simple structure and relies on weaker convergence conditions. Finally, some numerical examples and an application in fuzzy optimization show the effectiveness of the proposed neural network. [ABSTRACT FROM AUTHOR]

This paper addresses a nonsmooth aggregative game to control multiple noncooperative players, each with a nonsmooth cost function that depends not only on its own decision but also on some aggregate effect among all the agents. In addition, the decision of each player is restricted by private and coupling constraints. To address these concerns, a distributed generalized Nash equilibrium (GNE) seeking algorithm is proposed. Two features distinguish our methods from the existing GNE seeking algorithms. Firstly, an adaptive penalty method is introduced to drive each player's action to enter the set of private constraints. The adaptive term ensures automatic adjustment of penalty parameter based on the degree of constraint violation excluding any prior calculation. Secondly, a distributed dynamic event-triggered mechanism is designed for each player to lessen communication energy. In comparison to the static event-triggered mechanism, the proposed dynamic mechanism possesses larger inter-execution time intervals. As the discontinuity of the event-triggered mechanism can impact the existence of a solution to the closed-loop system in the classical sense, we adapt a nonsmooth analysis technique, including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, the convergence result and the avoidance of Zeno behavior are established. Finally, two engineering examples are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]