While standard (nominal) model predictive control can react to disturbances, it has no explicit model of uncertainty. This is not sufficient to ensure robust constraint satisfaction, as a trajectory at the boundary of the feasible set can be tipped into infeasibility by a small perturbation. There are two main paradigms for uncertainty-aware MPC: stochastic MPC (SMPC) and robust MPC (RMPC). In both approaches, knowledge of the uncertainty is included in the system model and the optimal control problem (OCP) formulation. The specific challenges of both approaches are closely related: (a) the propagation of uncertainty sets through time, (b) fulfilling constraints with respect to these uncertainty sets and (c) the optimization over feedback policies to avoid the prediction of unreallistically fast growing uncertainty sets. By surmounting these challenges, one can ensure that an appropriate back-off is kept from constraints without the need for hand-engineered and heuristically chosen safety margins.

However, in their standard forms both RMPC and SMPC only consider static uncertainty estimates: they are not aware that uncertainty may be reduced by learning about the system. This is the topic of the field of dual control: how can the conflicting objectives of exploration to learn about the system dynamics and exploitation of the obtained knowledge be balanced? And more specifically: how can this trade-off be captured by the optimal control problem formulation, such that the trade-off is automatically optimally resolved without the need for heuristic problem modifications?

The focus of my PhD is on both efficient formulations and algorithms for uncertainty-aware (stochastic, robust, dual) optimal control and model predictive control. These two aims go hand in hand, as exploitation of the specific structure of a formulation is the basis for tailored algorithms.