On the identification of linear time invariant systems with guaranteed simulation error bounds

The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise with unknown bound, and a finite set of data is available for parameter estimation. The goal is to derive a model with guaranteed simulation error bounds for all predicted time steps, up to a finite horizon of choice. This is achieved in three steps. At first, the noise bound, system order, and impulse response decay rate are estimated from data. Then, the estimated quantities are used to refine the sets of all possible multi-step predictors compatible with data and prior assumptions (Feasible Parameter Sets, FPSs). The FPSs allow one to derive, in a Set Membership framework, guaranteed error bounds for any given multi-step predictor, including the one obtained by simulating the system model. Finally, the wanted model parameters are identified by numerical optimization, imposing the constraints provided by the FPSs and using one of two proposed optimality criteria. Numerical simulations illustrate the validity of the approach.