Input Selection for Performance and Controllability of Structured Linear Descriptor Systems.

A common approach to controlling complex networks is to directly control a subset of input nodes, which then controls the remaining nodes via network interactions. Current approaches for selecting input nodes assume that either all system matrix entries are known and fixed, or are independent free parameters, and focus either on performance or controllability. In this paper, we make two contributions towards input selection in networked systems. First, we propose polynomial-time algorithms for input selection in structured linear descriptor systems, which are systems with dependencies between free parameters due to physical laws or design constraints. Second, we develop a framework for input selection based on joint consideration of controllability and performance. We make both contributions by mapping input selection to a submodular optimization problem under two matroid constraints, which enables development of polynomial-time algorithms with provable optimality guarantees. We provide improved optimality guarantees for special cases such as strongly connected networks, consensus networks, double integrators, and networks where all system parameters can take any arbitrary real values.