博弈论框架下的二阶多智能体系统领导者选择算法

随着人工智能的发展,多智能体系统中智能体的异质性、工作环境的复杂性、系统目标的多样性,给多智能体系统动态性能的分析带来了挑战.同时,也催生了新的控制策略和优化方法.博弈论作为一种研究社会系统中智能体决策过程的经典工具,如今已被应用到了多智能体系统研究领域.本文主要针对二阶多智能体系统编队过程中领导者选取的两类问题:1)选取k个领导者使系统误差达到最小;2)系统误差在一定范围内,选取最小数量的领导者;提出了一类超模博弈建模方法.在建模过程中设计了各个智能体的效用函数与系统整体的目标函数,使各个智能体在寻求各自效用函数最大化的过程中实现整体目标.而后,运用贪婪算法优化了智能体决策过程.本文分析了所建模型的平衡点存在性和系统稳定性.最后,利用仿真实例对比说明了本文提出的基于超模博弈的二阶多智能体系统领导者选择算法的有效性.

Game theoretical approach for the leader selection of the second-order multi-agent system

With the development of the arti?cial intelligence, the features of Multi-agent System (MAS), such as het- erogeneous agents, complex environment, and objective variety, bring challenges for analysis the dynamics of the system. Therefore, new control policies and optimization methods are required to deal with the challenges. Game theory which is a classic tool for studying the decision making processes of the agents in social system is rising as a meaningful method for analyzing the dynamics of the MAS. Two kinds of leader selection problems which exist in the formation of second- order MAS are discussed. The supermodular game is introduced to model two kinds of leader selection problems, namely, the problem of selecting a ?xed number of leaders in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. As to the designed supermodular game theoretical model, the utility functions and objective functions of the agents are designed. The global objective function can be achieved by maximizing utility function of the agents. Moreover, the greedy algorithm is pro- posed to optimize the decision making processes of the agents. The analytical properties of the designed model are also discussed. Simulation examples are provided to illustrate the effectiveness of the designed game theoretical model.