Scenario-based approach to stochastic linear predictive control

In this paper we consider the problem of predictive control for linear systems subject to stochastic disturbances. We repeatedly solve a stochastic finite-time constrained optimal control problem by using the scenario-based approach. We address the conservatism of the approach by presenting a new technique for fast scenario removal based on mixed-integer quadratic optimization. Probabilistic bounds are derived which quantify the benefits of the proposed technique. The approach is illustrated through a numerical example.