On the Design of Integral Multiplex Control Protocols for Nonlinear Network Systems with Delays

We consider the problem of designing control protocols for possibly nonlinear networks with delays that not only allow the fulfilment of some desired behaviour but also simultaneously guarantee the rejection of polynomial disturbances and the non-amplification of other classes of disturbances across the network. To address this problem, we propose the systematic use of multiplex architectures to deliver integral control protocols ensuring the desired disturbance rejection and non-amplification properties. We then present a set of sufficient conditions to assess these properties and hence to design the multiplex architecture for both leaderless and leader-follower networks with time-varying references consisting of possibly heterogeneous nonlinearly coupled agents affected by communication delays. The effectiveness of our conditions, which are also turned into an optimisation problem allowing protocol design, is illustrated via both in-silico and experimental validations with a real hardware set-up.