An extended output error recursive algorithm for identification in closed loop

The joint problem of recursive estimation of an optimal predictor for a closed loop system and unbiased estimation of the plant model parameters in closed loop operations is considered. An extended output error predictor for the closed loop is introduced. This allows us to derive a parameter estimation algorithm for the plant model which is globally asymptotically stable in a deterministic environment, guarantees, the convergence toward the optimal linear predictor of the closed loop and gives asymptotically unbiased parameters estimates under richness conditions. The paper presents a stability analysis in a deterministic environment and a convergence analysis in a stochastic environment. A simulation example illustrates the performances of the proposed algorithm