Stochastic Model Predictive Control using Initial State and Variance Interpolation

Abstract: We present a Stochastic Model Predictive Control (SMPC) framework for linear systems subject to Gaussian disturbances. In order to avoid feasibility issues, we employ a recent initialization strategy, optimizing over an interpolation of the initial state between the current measurement and previous prediction. By also considering the variance in the interpolation, we can employ variable-size tubes, to ensure constraint satisfaction in closed-loop. We show that this novel method improves control performance and enables following the constraint closer, then previous methods. Using a DC-DC converter as numerical example we illustrated the improvement over previous methods.