论文标题
控制与对称性的网络共识
Controlling consensus in networks with symmetries
论文作者
论文摘要
我们研究具有线性动力学的网络，其中对（a，b）的对称性的存在诱导簇中网络节点的分区，而矩阵A不限于以拉普拉斯的形式进行。对于这些网络，可以定义一个不变的组共有子空间，其中同一群集中的节点在时间上沿着相同的轨迹演变。我们证明，网络动力学在与此子空间正交的方向上是无法控制的。在假设与此子空间平行的动力学是可控的，我们设计了将组共识动态驱动到所需状态的最佳控制器。然后，我们考虑选择稳定组共识子空间的其他控件输入的问题，并在此目的的最小额外输入和驱动程序节点上获得界限。总之，我们的结果表明，可以独立设计沿着组共识子空间的控制动作并横向设计。
We study networks with linear dynamics where the presence of symmetries of the pair (A,B) 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 stabilize 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 design independently the control action along and transverse to the group consensus subspace.
