Can performance be always improved in iterative identification/control designs: a case study

Considers certainty equivalence control design for a high order plant on the basis of an estimate that is identified within a less complexity model set. Application of a closed loop identification together with successive controller design based on the obtained estimate is repeated. The following questions are addressed: (1) Does performance improve after each identification/control design interaction? (2) Does there exist an integer l>0 so that performance improves after every l interaction? (3) Does performance improve asymptotically? Through a case study, the author shows that the answer to all the above three questions is “not always”. The author then provides discussions as to how performance improvement might be noticed