Learning multi-step prediction models for receding horizon control

In this paper, the derivation of multi-step-ahead prediction models from sampled input-output data of a linear system is considered. Specifically, a dedicated prediction model is built for each future time step of interest. Each model is linearly parametrized in a suitable regressor vector, composed of past output values and past and future input values. In addition to a nominal model, the set of all models consistent with data and prior information is derived as well, making the approach suitable for robust control design within a Model Predictive Control framework. The resulting parameter identification problem is solved through a sequence of convex programs. Convergence of the identified error bounds to their theoretical minimum is demonstrated, under suitable assumptions on the measured data, and features like worst-case accuracy computation are illustrated in a numerical example.