Open AccessNecessary and sufficient characterisation for output synchronisation of linear heterogeneous agents using reflexive generalised inverses
Author(s) -
Kim Hongkeun
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5622
Subject(s) - linear subspace , constraint (computer aided design) , control theory (sociology) , mathematics , interpretation (philosophy) , stability (learning theory) , state (computer science) , linear system , reflexivity , computer science , mathematical optimization , algorithm , pure mathematics , mathematical analysis , artificial intelligence , geometry , control (management) , machine learning , programming language , social science , sociology
This work studies the conditions on which the outputs of linear heterogeneous (i.e. non‐identical) agents are asymptotically synchronised, where the dynamics of the agents and the dimensions of the state variables might widely differ among themselves. With the constraint that the relative outputs of the agents are the only measurements, it is shown that the reflexive generalised inverses play a key role in characterising the conditions, and give rise to the synchronisation stability of the agents. Together with the internal model principle for synchronisation, this results in a necessary and sufficient condition for reaching the asymptotic output synchronisation. This necessary and sufficient characterisation has its own geometric interpretation as the reflexive generalised inverses are related to the projections onto subspaces. Finally, it is shown that the condition is in fact a natural generalisation of the state synchronisability of homogeneous (i.e. identical) linear agents. A computer simulation is also provided to verify the result.