How Can We Be Robust Against Graph Uncertainties?

The article shows that it is possible to leverage relevant recent results developed in the area of identification of dynamic networks to introduce a notion of robustness with respect to uncertainties in the graph structure of a distributed system. It is assumed that in an observational framework, only a subset of the variables of a networked system are measured and the topology of the interconnections between the variables is not fully known. When the objective is designing a controller for the overall system, the topological uncertainties impede the exact identification of the overall open-loop transfer function and consequently, the exact design of the controller. It is shown, however, that some of the transfer functions of the network could be consistently identified using some sufficient and necessary graphical conditions and, in some cases, the overall open loop transfer function can be modeled by a term that can be consistently estimated and an uncertain term which is proven to be bounded. Consequently, this allows one to borrow control design techniques from the area of robust control.