Data-based Nominal Model Assessment for Robust Control under Measurement Noise

Prior information for robust control synthesis includes the knowledge of a nominal model and upper bounds on model uncertainties and external disturbances. Incomplete prior information is often an obstacle in the application of robust control theory to real problems. Data-based estimation of upper bounds on model uncertainties and disturbances is called errors quantification. At the early 90s, the role of errors quantification for robust control was characterized in [1] as follows: " To summarize, most of the present focus of research is on the estimation of error bounds. This problem is not only of independent interest, but it is also an important step towards the design of robust controllers based on identified models. However, I strongly believe that the key ingredient for the successful application of robust control design methods to identified models is not so much the computation of error bounds, but it is to let the global control performance criterion dictate what the identification criterion should be. " More than 10 years later M. Gevers wrote in [2]: " In the context of system identification, data-based estimation of model errors and noise properties from data is of interest in its own right; indeed, a reputable engineer should never deliver a model without a statement about its error margins. The activity on estimation of uncertainty sets was often erroneously put under the umbrella of identification for control, since in most of this work the control objective was not taken into account in the identification design. " The best identification criterion in control-oriented system identification, errors quanti-fication in particular, should be the global control performance criterion itself [3]. However , so strongly control-oriented approach to identification generally leads to insoluble or extremely difficult optimization problems. In the present paper the idea of treating the control criterion as the identification criterion is applied to the problem of data-based model assessment for robust tracking under assumption that the nominal model, in the form of single-input single-output LTI (linear time-invariant) discrete-time system, is given. The control criterion J is taken in the form of the worst-case steady-state tracking error. Given measurement data on some time interval, the problem of interest is to compute as small as possible data-consistent upper bound on the control criterion J under unknown upper bounds on coprime factor perturbations, external disturbance, and measurement noise. This problem implies the estimation of unknown upper bounds and the computation of respective optimal …