具有多图拓扑结构的同类智能体LQR控制

张冬梅; 欧琳琳; 孟莉; 王辛刚

doi:10.3724/SP.J.1004.2013.00913

具有多图拓扑结构的同类智能体LQR控制

doi: 10.3724/SP.J.1004.2013.00913

1.
浙江工业大学理学院杭州 310004;
2.
浙江工业大学信息工程学院杭州 310004

基金项目:

Supported by National Natural Science Foundation of China(61074039, 61273116, 1101367)

详细信息

通讯作者:
欧琳琳

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- 被引次数: 0
出版历程
- 收稿日期: 2012-08-13
- 修回日期: 2013-02-13
- 刊出日期: 2013-06-20

LQR Control for Homogeneous Agents with Multi-graph Topology

1.
College of Science, Zhejiang University of Technology, Hangzhou 310023, China;
2.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China

Funds:

Supported by National Natural Science Foundation of China(61074039, 61273116, 1101367)

摘要

摘要: 本文考虑具有一般线性时不变动态特性的多智能体系统优化控制问题. 将智能体之间的通讯拓扑结构建模成具有自环的无向多图, 每个子系统就是一个节点, 每个节点的控制行为只与本身及邻居节点有关. 由于反馈矩阵具有块对角结构约束, 本文研究的LQR控制问题本质上是一类结构优化问题. 最小化系统LQR性能指标等价于最小化单个智能体性能指标和. 基于线性矩阵不等式得到系统的次优性能指标, 指出LQR性能域是凸集. 由此多智能体系统的LQR控制转化为若干个子系统的LQR控制, 可以通过求解系数是Laplacian矩阵最小最大特征值的两个矩阵不等式得到反馈增益. 数值例子验证了方法的有效性.
- 多智能体系统 /
- 分解优化 /
- LQR 理论 /
- Lyapunov稳定性定理
Abstract: We consider a set of multi-agent systems (MASs) with general linear time-invariant (LTI) dynamics and a control problem where the performance index couples the behavior of the system. The interconnection topology between the agents is modeled as an undirected multi-graph with self-loop, where each system is a node and the control action at each node is a function of its state and the states of its neighbors. The linear quadratic regulator (LQR) control problem considered in this paper can be regarded as a structure optimization problem due to the block diagonal restriction on the feedback gain. It is shown that minimizing the LQR performance limit of the multiagent system under the distributed controller equals minimizing the sum performance of a single agent system. A sufficient condition is presented in terms of a set of linear matrix inequalities (LMIs) to achieve certain suboptimal performance specifications. In addition to make the control design more applicable, the notion of the LQR performance region is introduced and analyzed, which is shown to be convex with respect to the eigenvalues of the Laplacian matrix. The LQR control of the multi-agent system is then converted to the LQR control of a set of subsystems, which incorporates only two inequality constraints with the minimum and maximum eigenvalues as the coefficients. Numerical examples are presented to illustrate the proposed method.
- Multi-agent system (MAS) /
- decomposition optimization /
- linear quadratic regulator (LQR) theory /
- Lyapunov stability theory

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