In this paper, after closed loop system identification is reviewed, asymptotic analysis and finite sample analysis for closed loop system identification are studied respectively, corresponding to the infinite data and finite data. More specifically, within the framework of infinite data, the cost function is modified to its simplified form, and one optimal feedback controller is obtained based on our own derivations. The simplified cost function and optimal feedback controller are benefit for practical application. Furthermore, the asymptotic variance of that optimal feedback controller is also yielded from the point of asymptotic analysis. In the case of finite data, finite sample properties are constructed for closed loop system identification, then one difference between the sampled identification criterion and its corresponding expected criterion is derived as an explicit form, which can bound one guaranteed interval for the sampled identification criterion. Finally, one simulation example is used to prove the efficiency of our proposed theories.
Finite Sample Properties for Closed Loop System Identification
