System identification and adaptive control based on a variable regression for systems having unknown delay

An algorithm is presented for the recursive estimation of both process parameters and delay where no a priori knowledge of the delay is required. This algorithm is a modification of any standard recursive parameter estimation algorithm and can be applied easily to any of the well-established versions of estimation algorithms (least squares, instrumental variables, maximum likelihood, etc.) and their extensions. The algorithm requires minimum additional computations to the original algorithm. The delay is explicitly estimated and the parameter vector is of the same length as the undelayed system. This means clear separation between the system dynamics and delay. The proposed algorithm works in open-loop estimation and closed-loop adaptive control