Robust identification and control based on ellipsoidal parametric uncertainty descriptions

Connecting identification and controller design is a major challenge to modern control theory. Here, connection is made through ellipsoidal descriptions of parameter uncertainty. Identification is performed in the bounded-error context. H(infinity) techniques are then employed to maximize the size of an ellipsoid with the same center and shape and for which performance of the synthesized controller is guaranteed. It is always possible to choose the bound on the error in the estimation phase so that the two ellipsoids are identical. The resulting procedure can be seen as assuming the largest error bounds for which robust performance can still be guaranteed. A prototype algorithm is proposed, and applied to the flexible transmission used in a now classical benchmark. Although the experiment, a single closed-loop step response with an unknown controller in the loop, was much less informative than those performed to get the models used in the benchmark (open-loop experiments with pseudo-random binary sequences as input), a satisfactory performance in terms of closed-loop response could still be obtained.