Controllability and Observability of Evolving Directed Networks with Non-identical Linear Node Dynamics

Description

This proposal aims to study the controllability of evolving directed complex networks with non-identical linear node dynamics and to derive some precise graph-theoretic controllability conditions and criteria for such networks. The associated network observability property will also be investigated.Several basic settings and typical scenarios will be considered, including pinning control with one single controller (if it is sufficient) and with multiple controllers (if it can be more effective), respectively, for various topologies such as regular, random, small-world and scale-free networks. The effects of key parameters and network structures on the network controllability and observability will be explored and analyzed.Three research objectives are proposed to achieve: (1) for complex networks with one single pinning controller, derive some precise graphic-algebraic controllability conditions and examine the effects of various network parameters on the controllability; (2) for complex networks with multiple pinning controllers, derive some precise graphic-algebraic controllability conditions and investigate the effects of community structures on the controllability; and (3) similarly as above, derive some precise graphic-algebraic observability conditions and investigate the practical case with noisy measurements.