  Networked control strategies based on limited information about the plant
model usually results in worse closed-loop performance than optimal centralized
control with full plant model information. Recently, this fact has been
established by utilizing the concept of competitive ratio, which is defined as
the worst case ratio of the cost of a control design with limited model
information to the cost of the optimal control design with full model
information. We show that an adaptive controller, inspired by a controller
proposed by Campi and Kumar, with limited plant model information,
asymptotically achieves the closed-loop performance of the optimal centralized
controller with full model information for almost any plant. Therefore, there
exists, at least, one adaptive control design strategy with limited plant model
information that can achieve a competitive ratio equal to one. The plant model
considered in the paper belongs to a compact set of stochastic linear
time-invariant systems and the closed loop performance measure is the ergodic
mean of a quadratic function of the state and control input. We illustrate the
applicability of the results numerically on a vehicle platooning problem.
