Simplified approaches to polynomial design of model predictive controllers

Two approaches are proposed for obtaining a regularly partitioned piecewise polynomial that approximates the optimal model predictive controller. They are advantageous to obtaining the optimal model predictive controller in that they do not require geometric computation, which is problematic when the predicted horizon is long, the plant is of high order, or the piecewise structure is nearly degenerate. In each of the approaches, the design is formulated as a robust optimization problem, which is solved with the sum-of-squares method. They are improvement of the approach previously proposed by the same author and can be performed with smaller computational cost. Between the proposed two approaches, the first one requires smaller computational cost while the second one gives evaluation of the quality of approximation. A numerical example is provided for illustration.