Model Predictive Control (MPC), variously known as rolling-horizon control, receding-horizon control, etc, is a powerful technique employed in diverse engineering applications, and valued for its inherent ability to handle constraints while minimizing some cost (or maximizing some reward). The underlying idea of MPC is to approximate an infinite horizon constrained optimization problem by a finite horizon one, and then an optimal control law is calculated at every time step and applied in a rolling-horizon fashion. In most applications uncertainty in the model is involved, either due to some external disturbances or due to imprecise modeling of the controlled process. Uncertainty is commonly addressed in literature by formulating a robust MPC problem, assuming that the uncertainty is bounded and adopting a worst-case approach. Although there has been some major advances in this field, this approach is often too pessimistic.
But what happens if the uncertainty is not bounded? Or when it is not uniformly distributed? A less conservative approach would clearly be to take these possibilities into account, identifying appropriate distributions of the uncertainties and formulating a stochastic MPC problem instead. In this context, there are several points one should take into consideration for the problem formulation:
The main aim of the research in this group is to develop theoretical foundations of stochastic MPC, as well as to consider implementation issues, driven by some relevant applications. The aspects we currently focus on can be divided in the following areas: