【作者】 汪洋；

【导师】 周建平； 方木云；

【作者基本信息】 安徽工业大学 ， 计算机科学与技术， 2019， 硕士

【摘要】 近些年来,多智能体系统的一致性广泛应用于智能电网调度、卫星编队控制等领域。在一些实际应用场合,多智能体系统的通讯拓扑结构经常不断变化,并且随机噪声往往难以避免。这对多智能体系统的性能具有很大影响,可能导致整个系统无法实现一致。因此,本文基于平均驻留时间(ADT)切换拓扑,对几类随机多智能体系统的一致性问题展开了研究,并获得了一些结果,主要工作总结如下:(1)研究一类离散时间随机多智能体系统H_-∞一致性问题。旨在设计一个静态输出反馈控制协议,使得系统均方一致且满足一个预定的加权H_-∞扰动抑制指标。首先,通过引入线性变换,将闭环系统转化为一个降阶系统,并将H_-∞一致性问题转化为一个H_-∞控制问题。随后给出了关于这一降阶系统均方渐近稳定性和加权∞H性能的判据。在此基础上,提出了静态输出反馈控制协议的设计方法。期望的控制增益矩阵可通过一些线性矩阵不等式(LMIs)可行解予以获取。最后,借助一个数值算例验证了所得结果的有效性。(2)研究一类非线性随机多智能体系统H_-∞一致性问题。旨在设计一个动态输出反馈控制协议,使得系统均方一致且满足一个预定的加权H_-∞扰动抑制指标。对系统施加模型变换,将H_-∞一致性问题转化为一个降阶系统的H_-∞控制问题。然后,应用Lyapunov函数方法结合非线性处理技巧,给出了关于这一降阶系统均方渐近稳定性和加权H_-∞性能的一个判据。在此基础上,提出了动态输出反馈控制协议的设计策略。期望的控制增益矩阵可通过一些LMIs的可行解予以获取。最后,借助一个数值算例验证了所得结果的有效性。(3)研究一类时延随机多智能体系统-L_-2-L_-∞一致性问题。旨在设计一个观测器控制协议,使得系统均方一致且满足一个预定的加权-L_-2-L_-∞扰动抑制指标。首先,通过引入线性变换,将-L_-2-L_-∞一致性问题转化为降阶时延系统-L_-2-L_-∞控制问题。然后,应用Lyapunov-Krasovskii泛函方法及一些随机分析技巧,给出了这一降阶时延系统均方渐近稳定性和加权-L_-2-L_-∞性能的判定条件。在此基础上,提出了观测器控制协议的设计方法。期望的控制增益矩阵可通过一些LMIs的可行解予以获取。最后,借助一个数值算例验证了所得结果的有效性。更多还原

【Abstract】 In recent years,the consensus of multi-agent systems has been widely used in smart grid dispatching,satellite formation control and other fields.In some practical applications,the communication topology of a multi-agent system is constantly changing,and stochastic noise is often unavoidable.These two factors have a great impact on the performance of multi-agent systems and may lead to the failure of the whole system to achieve consensus.Based on the average dwell-time(ADT),this thesis studies the consensus of several different types of stochastic multi-agent systems and obtains some results.The main work is summarized as follows:(1)The problem of H_-∞consensus of a class of discrete-time stochastic multi-agent systems is studied.The purpose of this thesis is to design a static output-feedback control protocol such that the system achieves mean-square consensus and satisfies a predetermined weighted H_-∞ disturbance attenuation index.Firstly,by introducing a linear transformation,the closed-loop system is transformed into a reduced-order system and the problem of H_-∞ consensus is transformed into a H_-∞control problem.Then criteria for the mean-square asymptotic stability and weighted H_-∞ performance of the reduced-order system are given.Based on these results,a design method of the static output-feedback control protocol is proposed.The expected control gain matrix can be obtained by the feasible solutions of linear matrix inequalities(LMIs).Finally,a numerical example is given to verify the validity of the obtained results.(2)The problem of H_-∞ consensus of a class of nonlinear stochastic multi-agent systems is studied.The purpose of this thesis is to design a dynamic output-feedback control protocol such that the system achieves mean-square consensus and satisfies a predetermined weighted H_-∞ disturbance attenuation index.By applying model transformation to the system,the problem H_-∞ consensus is transformed into a H_-∞ control problem of reduced-order system.Then criteria for the mean-square asymptotic stability and weighted H_-∞ performance of the reduced-order system is given by using Lyapunov method and the technique of dealing with nonlinear.Based on these results,a design method of the dynamic output feedback control protocol is proposed.The expected control gain matrix can be obtained by some feasible solutions of linear matrix inequalities.Finally,a numerical example is given to verify the validity of the obtained results.(3)The problem of -L_-2-L_-∞ consensus of a class of stochastic multi-agent systems with time-delay is studied.The purpose of this thesis is to design a observer-based control protocol such that the system achieves mean-square consensus and satisfies a predetermined weighted -L_-2-L_-∞ disturbance attenuation index.Firstly,by introducing a linear transformation,the problem -L_-2-L_-∞ consensus is transformed into the -L_-2-L_-∞ control problem of reduced-order time-delay systems.Then,using Lyapunov-Krasovskii functional method and some stochastic analysis techniques,the criteria for determining mean-square asymptotic stability and weighted performance of the reduced-order time-delay systems are given.Based on these results,a design method of observer-based control protocol is proposed.The expected control gain matrix can be obtained by some feasible solutions of linear matrix inequalities.Finally,a numerical example is given to verify the validity of the obtained result.更多还原