  The design of optimal disturbance accommodation and servomechanism
controllers with limited plant model information is considered in this paper.
Their closed-loop performance are compared using a performance metric called
competitive ratio which is the worst-case ratio of the cost of a given control
design strategy to the cost of the optimal control design with full model
information. It was recently shown that when it comes to designing optimal
centralized or partially structured decentralized state-feedback controllers
with limited model information, the best control design strategy in terms of
competitive ratio is a static one. This is true even though the optimal
structured decentralized state-feedback controller with full model information
is dynamic. In this paper, we show that, in contrast, the best limited model
information control design strategy for the disturbance accommodation problem
gives a dynamic controller. We find an explicit minimizer of the competitive
ratio and we show that it is undominated, that is, there is no other control
design strategy that performs better for all possible plants while having the
same worst-case ratio. This optimal controller can be separated into a static
feedback law and a dynamic disturbance observer. For constant disturbances, it
is shown that this structure corresponds to proportional-integral control.
