Adaptive Control of Linear Time-Varying Plants: A New Model Reference Controller Structure

In this paper we study the problem of developing a control law which can force the output of a linear time-varying plant to track the output of a stable linear time-invariant reference model. We first show that the standard model reference controller, used for linear time-invariant plants, cannot guarantee zero tracking error in general when the plant is time-varying. We then propose a new model reference controller which guarantees stability and zero tracking error for a general class of linear time-varying plants with known parameters. When the time-varying plant parameters are unknown but vary slowly with time, we show that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean. The assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori. Such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters.