随机多智能体系统的一致性及优化控制

The problem of consensus for stochastic multi-agent systems is one hot problems of systems and control research at present. Until now relative research mainly focus at stochastic multi-agent systems modeled by first-order and second-order integral system, and the major research is the problem of consensus for systems with random switching topologies. There has been very little research on stochastic multi-agent systems modeled by general linear dynamics, and most research did not consider problems of finite-time consensus and optimal control, and the time-delay impacts on the system. The project plans to reaserch consensus problems, H-infinity consensus problems, finite-time consensus problems and optimal control problems for general dynamic multi-agent systems. For random switching topologies, the existence of stochastic disturbance, the changes of the number of agents and the existence of the time-delay for information transmission, different protocols will be designed, and then the consensus problems will be investigated by stochastic analysis, random graph, stochastic stability, random optimal control theory, robust control theory and so on. Finally, the reasonability of the obtained results will be verifief by computer simulation experiment. The project is deepening and develops of the research on consensus of multi-agent systems, and has obvious characteristics and innovation.

随机多智能体系统的一致性问题是目前系统与控制研究的热点之一。近些年，主要针对用一阶和二阶积分器描述的随机多智能体系统进行研究，主要研究拓扑结构随机切换系统的一致性问题。关于基于一般线性动力学的随机多智能体系统的研究非常少，并且大部分结果都没有考虑有限时间一致性问题，最优控制问题以及时滞对系统的影响。本项目拟研究一般动态多多智能体系统的一致性问题及H无穷一致性问题、有限时间一致性问题和最优控制问题。分别针对拓扑结构随机切换、存在随机干扰、智能体个数变化及存在信息传输时滞等情况，设计不同的控制协议，利用随机分析、随机图、随机稳定性、随机最优控制理论和鲁棒控制等，研究系统的一致性问题、H无穷一致性问题、有限时间一致性问题和最优控制问题。最后，利用计算机仿真实验验证所得结果的合理性。本项目是目前人们研究多智能体系统一致问题的自然深入和发展，具有明显的特色和创新性。

本项目研究了一般线性动力学随机多智能体系统的一致性问题，有限时间一致性，H无穷一致性问题和最优控制问题。对于一般线性多智能体系统，研究了带有干扰的离散和连续的多智能体的一致性问题；对于有限时间一致问题，研究了多目标环绕控制和事件触发两种情况下的一致性问题；对于H无穷一致问题，研究了二阶离散多智能体系统拓扑结构随机切换和带有干扰两种情况下的鲁棒一致问题；同时还研究了异质多智能体系统在拓扑结构随机切换下和带有干扰两种情况下的一致性问题。针对不同的情况，设计不同的控制协议，利用几何图论、随机分析、随机稳定性理论、随机最优控制理论、鲁棒控制等进行分析。同时利用仿真实验来验证结果的有效性。