Joint performance and controllability of networked systems

Abstract

Controllability is a basic requirement for control of networked systems. This chapter presents a framework for joint input selection based on joint optimization of performance and controllability. Standard conditions for controllability are discussed, including matrix pencil, controllability Gramian, and graph-theoretic conditions. The main contribution of this chapter is a formulation of controllability conditions as matroid constraints, enabling joint optimization of performance and controllability as a submodular maximization problem with matroid constraints. A graph controllability index is given, which characterizes the largest controllable subgraph of the network, and its submodular structure is proved. Application of this approach to consensus networks is discussed.