Online k-step model identification with directional forgetting

We propose a k-step ahead prediction recursive algorithm for online adaptive identification of slowly time-varying nonlinear systems based on polynomial NARX models to be used in model predictive control (MPC). In view of the possible mismatch between level of excitation and number of model parameters during online operation, we propose to initialize the model by an offline identification with sufficient excitation and then to use directional forgetting to update its parameters in closed loop under insufficient excitation in order to avoid estimator windup. We show the effectiveness and robustness with respect to disturbance properties such as noise color of the presented recursive algorithm by simulation examples in open and closed loop.