Indirect adaptive model predictive control and its application to uncertain linear systems

Abstract

SummaryWe consider constrained systems that are represented by uncertain models with unknown constant or slowly varying parameters. We propose an indirect adaptive model predictive control (IAMPC) approach where the prediction model can be adjusted during controller operation by a separately designed estimator that satisfies only a minimal set of assumptions. The controller guarantees constraint satisfaction despite the uncertainty in the parameters by means of a robust control invariant set, and input‐to‐state stability with respect to the estimation error by means of an appropriately designed method for adjusting the IAMPC prediction model and cost function based on the evolution of the parameter estimate. The controller has minimal computational overhead with respect to a nominal MPC and for the special case of uncertain linear systems, we obtain a constructive design procedure for the IAMPC which only solves quadratic programs during closed‐loop control.