Stability and Performance for Two Classes of Time-Varying Uncertain Plants
In this thesis, we consider plants with uncertain parameters where those parameters may be time-varying; we show that, with reasonable assumptions, we can design a controller that stabilizes such systems while providing near-optimal performance in the face of persistent discontinuities in the time-varying parameters. We consider two classes of uncertainty. The first class is modeled via a (possibly infinite) set of linear time invariant plants - the uncertain time variation consists of unpredictable (but sufficiently slow) switches between those plants. We consider standard LQR performance, and, in the case of a finite set of plants, the more complicated problem of LQR step tracking. Our second class is a time-varying gain margin problem: we consider an reasonably general, uncertain, time-varying function at the input of an otherwise linear time invariant nominal plant. In this second context, we consider the tracking problem wherein the signal to be tracked is modeled by a (stable) filter at the exogenous input and we measure performance via a weighted sensitivity function. The controllers are periodic and mildly nonlinear, with the exception that the controller for the second class is linear.