混合阶多智能体系统的一致控制
摘要
本文研究了混合1、2阶异质多智能体系统的一致性问题。提出了离散时间多智能体系统和连续时间多智能体系统的拟平均一致性问题及其控制协议。
对于离散时间混合阶多智能体系统,提出了基于差分方程的一致性协议。由稳定性分析,可以得到结论:如果多智能体系统的网络拓扑结构是连通的且平衡的,且步长不大于1 d max(G ),那么应用所提出的一致性协议,可以使多智能体系统达到拟平均一致。在Matlab中仿真了具有变拓扑无向网络结构的多智能体系统,步长?分别取0.1,0.25,0.33,0.34,并绘制了位置和速度曲线图以及相应的位置不一致函数V =δx( k)2曲线。从仿真结果可以看出,随着步长?的增加,系统达到一致所需要的时间也增加。当步长?取0.34,仅稍大于1 d max(G )时,多智能体系统便不再达到拟平均一致,位置的不一致函数曲线也表明了这一点。仿真结果证明了理论分析的有效性。
对于连续时间混合阶多智能体系统,提出了基于微分方程的一致性协议。讨论了4种情况:(1)定拓扑无向网络,(2)变拓扑无向网络,(3)定拓扑有向网络,(4)变拓扑有向网络下的稳定性。如果多智能体无向网络拓扑图是连通图,或者有向网络拓扑图是平衡图,那么应用所提出的协议可以解决异质多智能体系统的拟平均一致性问题。在变拓扑网络结构的稳定性分析中,提出了基于不一致向量δ( t)的Lyapunov函数V =δ(t )2,并应用Lyapunov稳定性理论讨论了变拓扑网络结构的稳定性。在Matlab中仿真了6个智能体4种拓扑结构的无向网络和有向网络两种情况,并绘制了不一致量δ( t)的函数V =δ(t )2曲线。仿真结果证明了理论分析的有效性。
分析中应用了代数图论,矩阵理论,Lyapunov稳定性理论等分析工具。
In this paper, consensus problems for multi-agents networks with heterogeneous nodes of mixed first and second order integrator is covered. Quasi-average consensus problem and corresponding consensus protocols for multi-agents systems with discrete time and continuous time are proposed.
For heterogeneous multi-agents system with discrete time, protocol based on difference equation is put forward. In convergence analysis, this conclusion can be proved: If network topology with multi-agents system is connectivity and balanceable, and step is not more than 1 d max(G ), then multi-agents system can reach quasi-average consensus based on protocol we put forward. Multi-agents system with switching topology undirected network is simulated in Matlab. Step value is selected by 0.1, 0.25, 0.33 and 0.34 in simulation, and position disagreement function is V =δx( k)2. From the simulation results, we can draw the conclusion: the time which multi-agents systems reach consensus is longer and longer along with increased steps? . When step is 0.34 which is little more than 1 d max(G ),multi-agents system can’t reach quasi-average consensus. The curve of position disagreement function also shows this conclusion. The simulation results show the obtained theoretical results.
For heterogeneous multi-agents system with continuous time, protocol based on difference equation is presented. 4 cases are analyzed: 1) undirected networks with fixed topology, 2) undirected networks with switching topology, 3) directed networks with fixed topology, and 4) directed networks with switching topology. If undirected networks of multi-agents systems are connective or directed networks of multi-agents systems are balance, then the quasi-average consensus can reach with corresponding protocol we presented. Lyapunov function V =δ( t)2 with disagreement vectorδ( t) is proposed in stability analysis for switching topology. The stability of multi-agents systems with switching topology is discussed using Lyapunov stability theory. Two cases of undirected and directed networks with 4 switching topology based on 6 agents are simulated in Matlab. The curves of function V =δ( t)2 with disagreement vectorδ( t) also show. Simulation results are testified that demonstrate the effectiveness of our theoretical results.
Our analysis framework is based on algebraic theory, matrix theory and Lyapunov stability theory.
对于离散时间混合阶多智能体系统,提出了基于差分方程的一致性协议。由稳定性分析,可以得到结论:如果多智能体系统的网络拓扑结构是连通的且平衡的,且步长不大于1 d max(G ),那么应用所提出的一致性协议,可以使多智能体系统达到拟平均一致。在Matlab中仿真了具有变拓扑无向网络结构的多智能体系统,步长?分别取0.1,0.25,0.33,0.34,并绘制了位置和速度曲线图以及相应的位置不一致函数V =δx( k)2曲线。从仿真结果可以看出,随着步长?的增加,系统达到一致所需要的时间也增加。当步长?取0.34,仅稍大于1 d max(G )时,多智能体系统便不再达到拟平均一致,位置的不一致函数曲线也表明了这一点。仿真结果证明了理论分析的有效性。
对于连续时间混合阶多智能体系统,提出了基于微分方程的一致性协议。讨论了4种情况:(1)定拓扑无向网络,(2)变拓扑无向网络,(3)定拓扑有向网络,(4)变拓扑有向网络下的稳定性。如果多智能体无向网络拓扑图是连通图,或者有向网络拓扑图是平衡图,那么应用所提出的协议可以解决异质多智能体系统的拟平均一致性问题。在变拓扑网络结构的稳定性分析中,提出了基于不一致向量δ( t)的Lyapunov函数V =δ(t )2,并应用Lyapunov稳定性理论讨论了变拓扑网络结构的稳定性。在Matlab中仿真了6个智能体4种拓扑结构的无向网络和有向网络两种情况,并绘制了不一致量δ( t)的函数V =δ(t )2曲线。仿真结果证明了理论分析的有效性。
分析中应用了代数图论,矩阵理论,Lyapunov稳定性理论等分析工具。
In this paper, consensus problems for multi-agents networks with heterogeneous nodes of mixed first and second order integrator is covered. Quasi-average consensus problem and corresponding consensus protocols for multi-agents systems with discrete time and continuous time are proposed.
For heterogeneous multi-agents system with discrete time, protocol based on difference equation is put forward. In convergence analysis, this conclusion can be proved: If network topology with multi-agents system is connectivity and balanceable, and step is not more than 1 d max(G ), then multi-agents system can reach quasi-average consensus based on protocol we put forward. Multi-agents system with switching topology undirected network is simulated in Matlab. Step value is selected by 0.1, 0.25, 0.33 and 0.34 in simulation, and position disagreement function is V =δx( k)2. From the simulation results, we can draw the conclusion: the time which multi-agents systems reach consensus is longer and longer along with increased steps? . When step is 0.34 which is little more than 1 d max(G ),multi-agents system can’t reach quasi-average consensus. The curve of position disagreement function also shows this conclusion. The simulation results show the obtained theoretical results.
For heterogeneous multi-agents system with continuous time, protocol based on difference equation is presented. 4 cases are analyzed: 1) undirected networks with fixed topology, 2) undirected networks with switching topology, 3) directed networks with fixed topology, and 4) directed networks with switching topology. If undirected networks of multi-agents systems are connective or directed networks of multi-agents systems are balance, then the quasi-average consensus can reach with corresponding protocol we presented. Lyapunov function V =δ( t)2 with disagreement vectorδ( t) is proposed in stability analysis for switching topology. The stability of multi-agents systems with switching topology is discussed using Lyapunov stability theory. Two cases of undirected and directed networks with 4 switching topology based on 6 agents are simulated in Matlab. The curves of function V =δ( t)2 with disagreement vectorδ( t) also show. Simulation results are testified that demonstrate the effectiveness of our theoretical results.
Our analysis framework is based on algebraic theory, matrix theory and Lyapunov stability theory.
引文
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