Controlling consensus in networks with symmetries
Controlling consensus in networks with symmetries
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DOI：
10.1080/00207179.2021.1946157
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发表时间：
2020-05
影响因子：
2.1
通讯作者：
F. L. Iudice;A. D. Meglio;F. D. Rossa;F. Sorrentino
中科院分区：
文献类型：
--
作者：
F. L. Iudice;A. D. Meglio;F. D. Rossa;F. Sorrentino
摘要：我们研究具有线性动力学的网络，其中对对称性的存在导致网络节点在簇中的划分，并且矩阵 A 不限于拉普拉斯形式。对于这些网络，可以定义一个不变的群体共识子空间，其中同一集群中的节点在时间上沿着相同的轨迹演化。我们证明网络动力学在与该子空间正交的方向上是不可控的。假设与该子空间平行的动态是可控的，我们设计了最优控制器，将群体共识动态推向期望的状态。然后，我们考虑选择附加控制输入的问题，以稳定群体共识子空间并获得为此目的所需的附加输入和驱动节点的最小数量的界限。总而言之，我们的结果表明，可以独立设计沿着和横向于群体共识子空间的控制动作。
ABSTRACT We study networks with linear dynamics where the presence of symmetries of the pair , induces a partition of the network nodes in clusters and the matrix A is not restricted to be in Laplacian form. For these networks, an invariant group consensus subspace can be defined, in which the nodes in the same cluster evolve along the same trajectory in time. We prove that the network dynamics is uncontrollable in directions orthogonal to this subspace. Under the assumption that the dynamics parallel to this subspace is controllable, we design optimal controllers that drive the group consensus dynamics towards a desired state. Then, we consider the problem of selecting additional control inputs that stabilise the group consensus subspace and obtain bounds on the minimum number of additional inputs and driver nodes needed to this end. Altogether, our results indicate that it is possible to independently design the control actions along and transverse to the group consensus subspace.