Adaptive model predictive control of nonlinear systems with state-dependent uncertainties

This paper studies adaptive model predictive control (AMPC) of systems with time-varying and potentially state-dependent uncertainties. We propose an estimation and prediction architecture within the min-max MPC framework. An adaptive estimator is presented to estimate the set-valued measures of the uncertainty using piecewise constant adaptive law, which can be arbitrarily accurate if the sampling period in adaptation is small enough. Based on such measures, a prediction scheme is provided that predicts the time-varying feasible set of the uncertainty over the prediction horizon. We show that if the uncertainty and its first derivatives are locally Lipschitz, the stability of the system with AMPC can always be guaranteed under the standard assumptions for traditional min-max MPC approaches, while the AMPC algorithm enhances the control performance by efficiently reducing the size of the feasible set of the uncertainty in min-max MPC setting. Copyright (C) 2017 John Wiley & Sons, Ltd.