Cooperative game theory-based steering law design of a CMG system

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

Modelling of a Human Driver’s Interaction with Vehicle Automated Steering Using Cooperative Game Theory

The introduction of automated driving systems raised questions about how the human driver interacts with the automated system. Non-cooperative game theory is increasingly used for modelling and understanding such interaction, while its counterpart, cooperative game theory is rarely discussed for similar applications despite it may be potentially more suitable. This paper describes the modelling of a human driver’s steering interaction with an automated steering system using cooperative game theory. The distributed Model Predictive Control approach is adopted to derive the driver’s and the automated steering system’s strategies in a Pareto equilibrium sense, namely their cooperative Pareto steering strategies. Two separate numerical studies are carried out to study the influence of strategy parameters, and the influence of strategy types on the driver’s and the automated system’s steering performance. It is found that when a driver interacts with an automated steering system using a cooperative Pareto steering strategy, the driver can improve his/her performance in following a target path through increasing his/her effort in pursuing his/her own interest under the driver-automation cooperative control goal. It is also found that a driver’s adoption of cooperative Pareto steering strategy leads to a reinforcement in the driver’s steering angle control, compared to the driver’s adoption of non-cooperative Nash strategy. This in turn enables the vehicle to return from a lane-change maneuver to straight-line driving swifter.

Diffusion mechanism simulation of cloud manufacturing complex network based on cooperative game theory

Cloud manufacturing is a specific implementation form of the "Internet + manufacturing" strategy. Why and how to develop cloud manufacturing platform(CMP), however, remains the key concern of both platform operators and users. A microscopic model is proposed to investigate advantages and diffusion forces of CMP through exploration of its diffusion process and mechanism. Specifically, a three-stage basic evolution process of CMP is innovatively proposed. Then, based on this basic process, a more complex CMP evolution model has been established in virtue of complex network theory, with five diffusion forces identified. Thereafter, simulations on CMP diffusion have been conducted. The results indicate that, CMP possesses better resource utilization,user satisfaction, and enterprise utility. Results of simulation on impacts of different diffusion forces show that both the time required for CMP to reach an equilibrium state and the final network size are affected simultaneously by the five diffusion forces. All these analyses indicate that CMP could create an open online cooperation environment and turns out to be an effective implementation of the "Internet + manufacturing" strategy.

A NOVEL COOPERATIVE SPECTRUM SENSING METHOD BASED ON COOPERATIVE GAME THEORY

A novel cooperative sensing method is proposed in this paper. The proposed scheme adopts sensing creditability degree to characterize the impact of the distance and the channel parameters on the sensing result,and considers that each user has different average SNR and different decision threshold,by using General Nash Bargaining Solution (GNBS) strategy in Cooperative Game Theory (CGT),the detection performance for two-user case are derived. For multi-user case,the sensing performance is obtained with Hungarian method. Compared with the traditional schemes such as Nash Bargaining Solution (NBS) and AND,the proposed scheme covers all the factors mentioned above,and enhances the sensing rationality and reliability. Simulation results show that the proposed scheme can further improve the sensing performance and creditability.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

A game-theory approach against Byzantine attack in cooperative spectrum sensing

In order to solve the Byzantine attack problem in cooperative spectrum sensing,a non-cooperative game-theory approach is proposed to realize an effective Byzantine defense.First,under the framework of the proposed non-cooperative game theory,the pure Byzantine attack strategy and defense strategy in cooperative spectrum sensing are analyzed from the perspective of the Byzantine attacker and network administrator.The cost and benefit of the pure strategy on both sides are defined. Secondly,the mixed attack and defense strategy are also derived. The closed form Nash equilibrium is obtained by the Lemke-Howson algorithm. Furthermore,the impact of the benefit ratio and penalty rate on the dynamic process of the noncooperative game is analyzed. Numerical simulation results show that the proposed game-theory approach can effectively defend against the Byzantine attack and save the defensive cost.

Game theory approach to optimal capital cost allocation in pollution control

This paper tries to integrate game theory, a very useful tool to resolve conflict phenomena, with optimal capital cost allocation issue in total emission control. First the necessity of allocating optimal capital costs fairly and reasonably among polluters in total emission control was analyzed. Then the possibility of applying game theory to the issue of the optimal capital cost allocation was expounded. Next the cooperative N person game model of the optimal capital cost allocation and its solution ways including method based on Shapley value, least core method, weak least core methods, proportional least core method, CGA method, MCRS method and so on were delineated. Finally through application of these methods it was concluded that to apply game theory in the optimal capital cost allocation issue is helpful to implement the total emission control planning schemes successfully, to control pollution effectively, and to ensure sustainable development.

Cooperative Differential Game for Model Energy-Bandwidth Efficiency Tradeoff in the Internet of Things

Internet of Things （IoT） refers to an infrastructure which enables the forms of com- munication and collaboration between people and things, and between things themselves. In order to improve its performance, we present a tradeoff between bandwidth and energy con- sumption in the loT in this paper. A service providing model is built to find the relation- ship between bandwidth and energy consump- tion using a cooperative differential game mo- del. The game solution is gotten in the condi- tion of grand coalition, feedback Nash equili- brium and intermediate coalitions and an allo- cation policy is obtain by Shapley theory. The results are shown as follows. Firstly, the per- formance of IoT decreases with the increasing of bandwidth cost or with the decreasing of en- ergy cost; secondly, all the nodes in the IoT com- posing a grand coalition can save bandwidth and energy consumption; thirdly, when the fac- tors of bandwidth cost and energy cost are eq- ual, the obtained number of provided services is an optimised value which is the trade-off between energy and bandwidth consumption.

Game Theory Algorithm of Reconfiguration for Shipboard Power System

船舶电力系统故障重构通过改变系统供电路径来恢复重要负载的供电，对增强系统的存活性有着重要意义。在多智能体（agent）架构的基础上，构建船舶电力系统博弈重构模型并提出求解方法。该模型以船舶电力系统中不同区域的agent作为博弈参与者，将船舶电力系统的重构问题转化为各agent之间的合作一竞争问题，从而保证重要负载的恢复供电。论文进一步提出该模型的求解算法，该算法首先判断博弈模式的合作与非合作属性，之后通过agent或agent联盟之间的博弈过程，计算各agent所属的负载／发电机的投切及转移策略。仿真算例表明，该算法能够快速有效地求解船舶电力系统重构问题，最大程度保证系统的存活性。

Bargaining Game Theoretic Power Control in Selfish Cooperative Relay Networks

Wireless cooperative communications require appropriate power allocation （PA） between the source and relay nodes. In selfish cooperative communication networks, two partner user nodes could help relaying information for each other, but each user node has the incentive to consume his power solely to decrease its own symbol error rate （SER） at the receiver. In this paper, we propose a fair and efficient PA scheme for the decode-and-forward cooperation protocol in selfish cooperative relay networks. We formulate this PA problem as a two-user cooperative bargaining game, and use Nash bargaining solution （NBS） to achieve a win-win strategy for both partner users. Simulation results indicate that the NBS is fair in that the degree of cooperation of a user only depends on how much contribution its partner can make to decrease its SER at the receiver, and efficient in the sense that the SER performance of both users could be improved through the game.

Cooperative Game Approach for Scheduling in Two-Virtual-Antenna Cellular Networks with Relay Stations Fairness Consideration

In thsssse cellular network, Relay Stations (RSs) help to improve the system performance; however, little work has been done considering the fairness of RSs. In this paper, we study the cooperative game approaches for scheduling in the wireless relay networks with two-virtual-antenna array mode. After defining the metric of relay channel capacity, we form a cooperative game for scheduling and present the interpretation of three different utilization objectives physically and mathematically. Then, a Nash Bargaining Solution (NBS) is utilized for resource allocation considering the traffic load fairness for relays. After proving the existence and uniqueness of NBS in Cooperative Game (CG-NBS), we are able to resolve the resource allocation problem in the cellular relay network by the relay selection and subcarrier assignment policy and the power allocation algorithm for both RSs and UEs. Simulation results reveal that the proposed CG-NBS scheme achieves better tradeoff between relay fairness and system throughput than the conventional Maximal Rate Optimization and Maximal Minimal Fairness methods.

A Game Theory Approach Using Excel

Understanding the behavior of companies in market conditions has been an important topic of studies for the economists and mathematicians. Many companies have treated their relationship of service providers as a game. Thus, the attitudes of the players can be endowed with rational thinking, which leads to the conclusion that the use of game theory as a tool to understand such behavior is of great importance. Based on the previous studies, this paper presents a study on the cooperative game theory, discussing the Nash equilibrium in pure and mixed strategies, treating solutions using the minimax John Von Neumarm theorem and illustrating a mathematical modeling of a game theory problem. Furthermore, a solution of linear programming using Microsoft Excel is also proposed and presented. The methodology adopted to model the problem may help students to familiarize themselves to game theory.

Game Theory Application and Strategic Bidding in Electricity Supply Market

This paper introduced the application of game theory in electricity power market. Moreover, the electricity pool model and the merit order dispatch method was introduced. In pool mode, participants are trying to maximize their benefit via competition with each other. Hence the market can be regarded as a non-cooperative game, especially, the electrical supply competition. Players (generators) could use strategic bidding to occupy advantages in competition. The bidding strategies of generators in electricity pool model were researched via build a 3-generator competition model. Moreover, Nash Equilibrium idea was used to explore generator’s optimal bidding strategy. The results show when players are in Nash Equilibrium;thestrategy is their optimal bidding strategy.

考虑碳排放分摊的综合能源服务商交易策略

为寻求在满足用户用能需求的同时降低系统碳排放的有效途径,提出了一种考虑碳排放分摊的多综合能源服务商能源交易策略。基于网络流模型实现碳流追踪并联合Shapley理论建立了综合能源服务商碳排放成本计算模型。应用Nash议价理论构建了多综合能源服务商合作博弈运行模型,将综合能源服务商碳排放成本引入优化目标函数,并利用分布式算法求解最优能源交易量和交易费用。基于由修改的IEEE 39节点电网和12节点气网构成的多综合能源服务商系统进行仿真分析,验证了所提模型和方法的有效性。

考虑新能源发电商租赁共享储能的电力市场博弈分析

针对实际中储能资源利用率不高等问题,提出一种新能源发电商和储能运营商之间的储能租赁共享模式,其中储能运营商除了租赁部分储能给新能源发电商外,还可利用剩余储能独立参与市场竞争,因而该模式有助于提高储能资源利用率。为了研究该共享模式对电力市场运行的影响,建立了考虑该共享模式的日前电力市场双层博弈模型,其中,上层为储能运营商与多个新能源发电商基于讨价还价博弈理论来确定储能租赁价格的优化模型,下层为新能源发电商、储能运营商与传统发电商作为价格影响者参与日前电力市场竞争的多时段非合作博弈模型。然后采用非线性互补方法将双层博弈模型转化为单层优化问题求解。最后通过算例仿真验证所提出租赁模式的合理性和有效性。

超模互补性对商业生态系统稳定的作用机制——基于合作博弈的模型构建与案例分析

如何在多元背景下构建和谐、稳定的商业生态系统战略联盟非常重要。基于合作博弈理论构建商业生态系统合作博弈模型,从理论上阐述超模互补性对生态系统稳定的作用机制,并以阿里巴巴商业生态系统为例进一步验证理论模型的关键结论。研究发现:商业生态系统参与者的直接收益和协同收益均具有超模属性;超模互补性在提升生态系统稳定性方面起着关键作用;更大的联盟中增加一个成员会为生态系统带来更多的收益增长;随着生态系统规模的增大,生态参与者从非股权协议转向接受投资入股形式时所获得的收益会增加。

基于共生理论的人机协同教育主体合作博弈及其优化策略研究

随着ChaGPT和大模型所代表的强人工智能技术驱动力的增强,中小学数字化课堂迈入人机协同教育智能观的里程碑阶段,教师可以把部分课堂活动交给机器教师独立完成,而人类教师处于监督活动过程的状态,从而形成了人机协同教育的复杂系统。如何厘清人和机主体之间背后的协同逻辑是人机协同教育中面临的新问题。首先,本研究基于共生理论的三要素,分析了人机协同教育系统的共生单元、共生模式和共生环境,然后根据协同任务的难易程度构建了人类教师与机器教师主体的合作博弈模型;其次,基于四个代表性变量值的变化,从合作博弈的角度探讨了六种人类教师和机器教师协同共生模式,从而为人机协同课堂教学设计提供了优化策略选择。最后,本研究选取某市基地学校小学三年级人机协同英语课中的一段场景,来分析人类教师和机器教师的博弈过程和结果,实践案例表明该合作博弈模型可优化教学策略,从而为人类教师和机器教师协同开展教学提供理论和实践参考。

基于自适应增强随机搜索的航天器追逃博弈策略研究

针对航天器与非合作目标追逃博弈的生存型微分对策拦截问题,基于强化学习研究了追逃博弈策略,提出了自适应增强随机搜索(adaptive-augmented random search,A-ARS)算法。针对序贯决策的稀疏奖励难题,设计了基于策略参数空间扰动的探索方法,加快策略收敛速度;针对可能过早陷入局部最优问题设计了新颖度函数并引导策略更新,可提升数据利用效率;通过数值仿真验证并与增强随机搜索(augmented random search,ARS)、近端策略优化算法(proximal policy optimization,PPO)以及深度确定性策略梯度下降算法(deep deterministic policy gradient,DDPG)进行对比,验证了此方法的有效性和先进性。

有人机/无人机协同作战效能的物元可拓评价

为提高有人机/无人机(MAV/UAV)的协同作战能力,提出一种基于物元可拓理论的MAV/UAV协同作战效能评价方法。该方法通过文献研究和作战体系分析,利用灰色关联与秩相关筛选过程,构建MAV/UAV协同作战效能评价指标体系;在博弈论基础上,平衡G1法权重与熵权法权重的主客观成分,完成评价指标的综合赋权;最后,结合非对称贴近度准则,建立MAV/UAV协同作战效能的物元可拓评价模型。结合作战案例进行评估与比对,得出敏感性影响因素,验证了方法的有效性和科学性,从而为MAV/UAV协同作战效能的正确评价提供了一种解决途径。

基于改进Shapley值法的风-光-水-储多主体互补发电系统合作增益分配策略

为了充分发挥系统中可调节资源的自身优势,利用变速抽水蓄能机组配合小水电机组进行常规调节,并考虑变速抽水蓄能机组的快速响应特性,提出了兼顾系统小时级以及秒级安全性的风-光-水-储多主体互补发电系统的联合优化调度模型。为了降低合作博弈高效性算法线性增长的计算复杂度,基于改进Shapely值法提出了一种大规模利益主体的合作增量效益(增益)分配策略。通过资源聚合,对高维度问题进行降维处理,利用Shapley值法进行初始分配;构建合作增益贡献指标,采用非对称纳什谈判理论对同类型的不同主体进行细化分配。以某流域风-光-水-储10主体互补发电系统为仿真算例,结果表明:抽水蓄能机组与小水电机组互补运行可以提升系统的灵活性和安全性;基于改进Shapley值法的合作增益分配策略具有计算高效性以及应用可行性。