Model Predictive Control with reduced number of variables for linear systems with bounded disturbances

Arising from the need to reduce online computations for Model Predictive controller, this paper proposes an approach for a linear system with bounded disturbance using fewer variables than the standard. The new variables are chosen based on the singular values of the matrix that maps the original variables to an affine subspace of the control inputs of the online optimization problem. Each new variable has an associated vector that corresponds to a right singular vector of the matrix. The motivation is to choose the variables that have the maximal amplification effect on the control inputs. Several other features are needed. These include an initialization procedure that recovers the original domain of attraction and an auxiliary state that ensures recursive feasibility of the online optimization problem. Computational advantage is demonstrated using several numerical examples.