Stealth identification strategy for closed loop linear time invariant system

Many identification strategies for closed loop linear time invariant system assume that an open loop system is closed by a feedback mechanism, which contains a known, linear time invariant controller. This assumption means that these identification strategies are feasible under some prior knowledge of feedback controller. To relax this assumption in some complex systems with unknown controller, a new stealth identification strategy is proposed to tackle the identification problem for closed loop linear time invariant system with unknown controller. Stealth identification modifies the closed loop system, so that the new prediction error and inverse covariance matrix are all independent of the unknown controller. This independence can simplify the problems of estimating parameter vector and designing optimal input. By using this simplified prediction error to construct an objective function, a candidate domain of attraction for the objective function is introduced and one convergence condition is derived to guarantee a given set be a candidate domain of attraction. Finally a simulation example confirms our theoretical results.