Pinning Controllability and Observability for Directed Networks of Non-identical Linear Node Systems with Multi-channel Connections

This proposal aims to study the controllability of directed complex networks with non-identical linear node dynamics which, differing from almost all existing settings, have multi-channel connections. The main objective is to derive some precise graph-theoretic controllability conditions and criteria for such practical networks. The dual topic of network observability will also be investigated. Several basic settings and typical scenarios will be considered, including networks with identical node systems and non-identical node systems, respectively, for various complex network topologies. The problem with external pinning control input by linear state-feedback controllers is considered, to find out how many and which nodes are needed to be pinned, so as to achieve the structural controllability of a general multi-channel directed network. Four technical objectives are proposed to achieve: (1) Demonstrate that the conclusion of strong structural network controllability is true for a general finite-sized directed network of identical nodes with multi-channel connections; (2) Extend the result obtained in Task 1 to a general finite-sized directed network of non-identical nodes; (3) Study the observability of the two settings described in (1) and (2), respectively; (4) Study the pinning controllability of the general setting of directed networks with multi-channel connections