Model validation and uncertainty modeling for linear multivariable robust control

Kyong Lim, NASA Langley

In applying mu analysis/synthesis to LTI systems, a nominal model, LFT uncertainty structure, and norm bounds on the model uncertainty and exogenous inputs are required a priori to define a particular set of plant models. If in addition input/output measurements are also available, this set can be checked for consistency, i.e., if this set could have generated the measured data, i.e., model validated (or not invalidated). The practical benefit of model validation is that it has a better chance of attaining designed robust performance in actual application. In this talk, we present an easily computable test for the existence of a model validating uncertainty set. Under mild conditions, this test is necessary and sufficient for the case of complex, nonrepeated, block-diagonal structure. For the more general case which includes repeated and/or real scalar uncertainties, this test is only necessary but becomes sufficient if a collinearity condition is also satisfied. If the test fails, it indicates either a lack of richness of the a priori uncertainty structure and/or that the exogenous noise/disturbance allowance is too small. If it passes, it is shown that a parameterization of all model validating sets of plant models with the given LFT structure is possible. The generally non-unique nature is recognized and the parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeoff among sets which have specific LFT structure. An optimization algorithm which seek a smallest model validating set of non-parametric uncertainties while subject to specified allowance levels for parametric uncertainties and noise/disturbance is proposed and demonstrated.