对称网络中的一致性控制
Controlling consensus in networks with symmetries
摘要：
我们研究线性动力学的网络，其中存在的对称性对（A，B）诱导集群中的网络节点的分区和矩阵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组共识子空间，其中同一簇中的节点沿着相同的轨迹演化。我们证明了网络动力学在与这个子空间正交的方向上是不可控的。假设平行于这个子空间的动态是可控的，我们设计的最优控制器，驱动组共识动态向一个期望的状态。然后，我们考虑的问题，选择额外的控制输入，稳定的群体共识子空间，并获得额外的输入和驱动节点的最小数量的界限，为此目的。总之，我们的研究结果表明，它是可能的独立设计的控制行动，沿和横向的群体共识子空间。
英文摘要：
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.
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