Dynamic Feedback Mean Square Consensus Control Based on Linear Transformation for Leader-follower Multi-agent Systems
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摘要: 研究了基于半马尔科夫(Markov)跳变的领导−跟随多智能体系统(Multi-agent system, MAS)的均方一致性控制问题. 首先, 针对多智能体系统同时存在通信时滞和执行器故障的问题, 提出基于线性变换的动态反馈控制策略. 其次, 将实现领导−跟随多智能体系统的均方一致性问题转化为多智能体误差系统的稳定性控制问题. 再次, 设计动态反馈控制器, 利用李亚谱诺夫(Lyapunov)函数抑制系统的非线性特性, 解决由控制器未知增益矩阵产生的非线性问题. 使领导−跟随多智能体系统达到均方一致, 并给出系统的
$ {H_{\infty} }$ 性能指标分析系统的鲁棒性. 最后, 仿真结果表明基于线性变换设计的动态反馈控制策略具有良好的控制性能, 并且能够提高领导−跟随多智能体系统的动态特性.-
关键词:
- 半Markov跳变系统 /
- 多智能体系统 /
- 动态反馈 /
- 线性变换 /
- 一致性控制
Abstract: This paper investigates the mean square consensus control for a class of multi-agent system (MAS) based on semi-Markov process. Firstly, a dynamic feedback control strategy based on the linear transformation is proposed to solve the problem of communication delay and actuator failure in the multi-agent system. Secondly, the mean square consensus control for the leader-follower multi-agent system is transformed into the stability control problem of the error system via the linear transformation. Thirdly, the dynamic feedback controller is designed to restrain the nonlinear characteristics of the multi-agent systems via Lyapunov functional, such that nonlinear problem caused by the unknown gain matrices is solved. Then, the dynamic feedback mean square consensus control of the leader-follower multi-agent system is achieved and the${H_{\infty} }$ performance index is proposed to analyze the robustness of the system. From the simulations, it can be seen that the dynamic feedback mean square consensus control based on linear transformation has better control performance, and the dynamic characteristics of the leader-follower multi-agent system is improved. -
图 2 状态变量
${{\boldsymbol{x}}_{i1}}( t )$ 响应曲线Fig. 2 The response of state variable
${{\boldsymbol{x}}_{i1}}( t )$ 
图 3 状态变量
${{\boldsymbol{x}}_{i2}}( t )$ 响应曲线Fig. 3 The response of state variable
${{\boldsymbol{x}}_{i2}}\left( t \right)$ 
图 4 系统误差
${\boldsymbol{e}}( t )$ 响应曲线Fig. 4 The response of system error
${\boldsymbol{e}}( t )$ 
图 7 状态变量
${{\boldsymbol{x}}_{i1}}\left( t \right)$ 响应曲线Fig. 7 The response of state variable
${{\boldsymbol{x}}_{i1}}\left( t \right)$ 
图 8 状态变量
${{\boldsymbol{x}}_{i2}}\left( t \right)$ 响应曲线Fig. 8 The response of state variable
${{\boldsymbol{x}}_{i2}}\left( t \right)$ 
图 9 系统误差
${\boldsymbol{e}}\left( t \right)$ 响应曲线Fig. 9 The response of system error
${\boldsymbol{e}}\left( t \right)$ 表 1
${\tau _M}$ 取不同值时$\gamma $ 对比结果Table 1 Comparison results of
$\gamma $ with different${\tau _M}$ 方法 ${\tau _M}$ 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 文献 [37] 0.5247 0.5470 0.5624 0.5885 0.6075 0.6276 0.6472 0.6603 0.6818 0.7022 定理 2 0.5050 0.5234 0.5475 0.5669 0.5849 0.6006 0.6254 0.6419 0.6657 0.6895 
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