Reducing variables in Model Predictive Control of linear system with disturbances using singular value decomposition

Arising from the need to reduce online computations of Model Predictive Controller, this paper proposes an approach for a linear system with bounded additive disturbance using fewer variables than the standard. The new variables are chosen so that they transfer the maximal energy to the control inputs. Several other features are introduced. These include an auxiliary state to ensure recursive feasibility, an initialization procedure that recovers a substantial portion of the original domain of attraction arising from the use of fewer variables. A comparison of the domains of attraction associated with the new variables is also discussed. Run-time computational advantage of more than an order of magnitude compared with standard approach is demonstrated using several numerical examples although a more expensive initialization is needed.