Stealth identification strategy for closed loop system structure

Many identification strategies for closed loop system structure assume that an open loop system is closed by a feedback mechanism, which contains a known and linear controller. This assumption means these identification strategies are feasible under some prior knowledge of feedback controller. To relax this assumption for some complex systems with unknown controller or nonlinear controller, a new stealth identification strategy is proposed to tackle the identification problem for closed loop system with unknown controller or nonlinear controller. Stealth identification modifies closed loop system, so that the new prediction error and inverse covariance matrix are all independent of the unknown controller or nonlinear controller. This independence simplifies the problem of estimating parameter vector and designing optimal input. The Robbins-Monro algorithm is applied to identify the unknown parameter vector in closed loop system with unknown controller, and the nonlinear controller is replaced by its equivalent linear time invariant controller. Some consideration about the linear approximation to nonlinear system are studied, and two linear approximation forms are constructed to approximate the nonlinear system. The effectiveness of our proposed stealth identification strategy is demonstrated through simulation example.