Control oriented H-infinity system identification based robust control design: An iterative procedure

Recently, research interest in robust control design philosophy has resulted in the development of several design tools and paradigms for synthesizing controllers that are robust to plant perturbations and modeling uncertainty. Of particular interest is the robust control design problem set in the {dollar}Hsb{lcub}infty{rcub}{dollar} (H-Infinity) paradigm, as a lot of desirable performance specifications and robustness properties are elegantly incorporated in this paradigm. Subsequently, {dollar}Hsb{lcub}infty{rcub}{dollar} control oriented system identification techniques have been developed to deliver system model descriptions compatible with {dollar}Hsb{lcub}infty{rcub}{dollar} robust control design techniques. To solve any modeling for control design problem in an optimal fashion, a tightly integrated identification and control design procedure is desirable.; In this thesis, we investigate the issues involved in integrating {dollar}Hsb{lcub}infty{rcub}{dollar} control oriented system identification methods with {dollar}Hsb{lcub}infty{rcub}{dollar} robust control design methods. Some convergence properties for successive iteration models derived using {dollar}Hsb{lcub}infty{rcub}{dollar} identification iteratively, are established. Weighted {dollar}Hsb{lcub}infty{rcub}{dollar} identification, which involves pre-filtering the frequency response data used by {dollar}Hsb{lcub}infty{rcub}{dollar} identification algorithms, is proposed to incorporate selective identification bandwidth and to deliver frequency dependent modeling error bounds. The notion of robustly stabilizable and robustly performant sets is defined, in terms of sets of models around the underlying system that are stabilized (and respectively that deliver the desired performance) with the same controller. The existence of these sets provides a convergence framework based on which an integrated, iterative, {dollar}Hsb{lcub}infty{rcub}{dollar} identification and {dollar}Hsb{lcub}infty{rcub}{dollar} robust control design procedure is developed. Each iteration in the proposed procedure involves weighted {dollar}Hsb{lcub}infty{rcub}{dollar} identification followed by {dollar}Hsb{lcub}infty{rcub}{dollar} robust control design, and an estimation of the desired improvement in model accuracy for the next iteration. The identification experiment and the weighting filter for the next modeling iteration are designed to achieve this increased accuracy. The proposed iterative procedure is tractable, computationally feasible and convergent.