Model predictive control with random variables of compound distributions and stochastic objective function

Stochastic model predictive control (SMPC) can be used in a broad variety of fields, such as diverse optimization problems. One issue which recently emerges is that some random variables contained in the objective function or probabilistic constraints will have compound distributions. The compound distributions are determined by some parameters which themselves are random and follow certain known distributions. This paper will propose an effective and intelligible way to compute compound distributions with the use of a similar logic to the Falling Shadow Theory. And to tackle the stochastic objective function, two typical formulations in risk studies, i.e., the value-at-risk (VaR) and conditional value-at-risk (CVaR), are introduced and formulated for SMPC. A simulation example regarding a coal trade decision-making process shows the efficacy of the proposed strategy.