Search Results (4)

Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model. Full article

In this paper, a distributed swarm control problem is studied for large-scale multi-agent systems (LS-MASs). Different than classical multi-agent systems, an LS-MAS brings new challenges to control design due to its large number of agents. It might be more difficult for developing the appropriate control to achieve complicated missions such as collective swarming. To address these challenges, a novel mixed game theory is developed with a hierarchical learning algorithm. In the mixed game, the LS-MAS is represented as a multi-group, large-scale leader–follower system. Then, a cooperative game is used to formulate the distributed swarm control for multi-group leaders, and a Stackelberg game is utilized to couple the leaders and their large-scale followers effectively. Using the interaction between leaders and followers, the mean field game is used to continue the collective swarm behavior from leaders to followers smoothly without raising the computational complexity or communication traffic. Moreover, a hierarchical learning algorithm is designed to learn the intelligent optimal distributed swarm control for multi-group leader–follower systems. Specifically, a multi-agent actor–critic algorithm is developed for obtaining the distributed optimal swarm control for multi-group leaders first. Furthermore, an actor–critic–mass method is designed to find the decentralized swarm control for large-scale followers. Eventually, a series of numerical simulations and a Lyapunov stability proof of the closed-loop system are conducted to demonstrate the performance of the developed scheme. Full article

This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control strategies. We derive the Nash mean-field-type equilibrium and cost in a linear state-and-mean-field feedback form by using a partial integro-differential system. Then, we examine the Stackelberg two-layer problem with multiple leaders and multiple followers. Numerical illustrations show that, in the symmetric case, having only one leader is not necessarily optimal for the total sum cost. Having too many leaders may also be suboptimal for the total sum cost. The methodology is extended to multi-level hierarchical systems. It is shown that the order of the play plays a key role in the total performance of the system. We also identify a specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. In the heterogeneous case, it is shown that the total cost is significantly affected by the design of the hierarchical structure of the problem. Full article

The IoT system has become a significant component of next generation networks, and drawn a lot of research interest in academia and industry. As the sensor nodes in the IoT system are always battery-limited devices, the power control problem is a serious problem in the IoT system which needs to be solved. In this paper, we research the resource allocation in the wireless powered IoT system, which includes one hybrid access point (HAP) and many wireless sensor nodes, to obtain the optimal power level for information transmission and energy transfer simultaneously. The relationship between the HAP and the sensor nodes are formulated as the Stackelberg game, and the dynamic variations of the energy for both the HAP and IoT devices are formulated through the dynamic game with mean field control. Then the power control in the wireless powered IoT system is formulated as a mean field Stackelberg game model. We aim to minimize the transmission cost for each sensor node based on optimally power resource allocation. Meanwhile, we attempt to minimize the energy transfer cost based on power control. As a result, the optimal solutions based on the mean field control of the sensor nodes and the HAP are achieved through dynamic programming theory and the law of large numbers, and $\epsilon$ -Nash equilibriums can be obtained. The energy variations for both the sensor nodes and HAP after the control of resource allocation based on the proposed approach are verified based on the simulation results. Full article