SET MEMBERSHIP IDENTIFICATION FOR H_∞ ROBUST CONTROL DESIGN

摘要

The Set Membership H_∞ identification of LTI discrete-time exponentially stable SISO systems, from noise corrupted measurements in the time and/or the frequency domain, is considered. The assumptions on the noise can account for information on its maximal magnitude and deterministic uncorrelation properties. A test is given for validating the assumptions on system and noise. The main focus of the paper is on the trade-off between identified model set complexity and optimality properties, and on the non conservativeness in the identification error evaluation. By using a suitably weighted H_∞ norm, the identification error measures the degradation of the closed loop performance that is underlying the control design, due to the mismatch between the actual plant and the model. Thus, optimality properties of the identified model set reflect in minimality of conservativeness of guaranteed closed loop performances. Identification of the optimal model set is a NP-hard problem and alternative algorithms are investigated, simpler to be computed, at the expense of identification accuracy degradation. This is measured by the suboptimality level of the identified model set, i.e. the ratio between the achieved identification error and the minimal one. A method is given to evaluate upper and lower bounds on this suboptimality level. Reduced order model sets that tightly include the optimal one are derived. Then, model set order selection can be performed by trading between model set complexity and suboptimality level degradation.