A conic reformulation of Model Predictive Control including bounded and stochastic disturbances under state and input constraints

Current state-of-the-art model predictive control does not provide means to handle stochastic disturbances in the presence of constraints. In this paper, we reformulate the MPC problem by bringing feed-back into the future prediction. This feedback is used to control the system response to bounded and stochastic disturbances. This eliminates the conservativeness of open-loop prediction-based dynamic optimization of uncertain stochastic systems in the presence of constraints. The resulting control framework alloys us to formulate the problem as a conic optimization. For conic problems numerically efficient algorithms exist, making on-line application of our strategy possible.