Adaptive Uncertainty Modeling: On-Line Robust Control Design

An approach is presented to the problem of designing a robust control using on-line measurements. The idea is to use standard methods of parametric system identification to obtain a nominal estimate of the plant transfer function. Non-parametric spectral methods are then used to obtain a frequency domian expression for model uncertainty. If the model uncertainty exceeds a specified frequency bound, which has been predetermined from the nominal model and the performance criteria, then data filters used in the system identification are modified and the proceedure is repeated. An analysis is presented which establishes conditions under which the proceedure will actually converge to a satisfactory robust design. An example is provided which illustrates the method and supporting analysis.