  In this paper, we develop a retrofit control method with approximate
environment modeling. Retrofit control is a modular control approach for a
general stable network system whose subsystems are supposed to be managed by
their corresponding subsystem operators. From the standpoint of a single
subsystem operator who performs the design of a retrofit controller, the
subsystems managed by all other operators can be regarded as an environment,
the complete system model of which is assumed not to be available. The proposed
retrofit control with approximate environment modeling has an advantage that
the stability of the resultant control system is robustly assured regardless of
not only the stability of approximate environment models, but also the
magnitude of modeling errors, provided that the network system before
implementing retrofit control is originally stable. This robustness property is
practically significant to incorporate existing identification methods of
unknown environments, because the accuracy of identified models may neither be
reliable nor assurable in reality. Furthermore, we conduct a control
performance analysis to show that the resultant performance can be regulated by
adjusting the accuracy of approximate environment modeling. The efficiency of
the proposed retrofit control is shown by numerical experiments on a network of
second-order oscillators.
