Stochastic Model Predictive Control using a combination of randomized and robust optimization

In this paper, we focus on Stochastic Model Predictive Control (SMPC) problems for systems with linear dynamics and additive uncertainty. One way to address such problems is by means of randomized algorithms. Typically, these algorithms require substituting the chance constraint of the SMPC problem with a finite number of hard constraints corresponding to samples of the uncertainty. Earlier approaches toward this direction lead to computationally expensive problems, whose solutions are typically very conservative in terms of cost. To address these limitations, we follow an alternative methodology based on a combination of randomized and robust optimization. We show that our approach can offer significant advantages in terms of both cost and computational time. Both the open-loop MPC formulation (i.e. optimizing over input sequences), as well as optimization over policies using the affine disturbance feedback formulation are considered. We demonstrate the efficacy of the proposed approach relative to standard randomized techniques on a building control problem.