ABSTRACT
This chapter considers standard approach and online approach. By standard approach it mean the usual approach, that is, in industrial Model predictive control (MPC) and most of the synthesis approaches of MPC, an finite-horizon optimization problem is solved and, in synthesis approaches, in general the three ingredients are selected off-line. In on-line approaches, one, two or all of the three ingredients are served as the decision variables of the on-line optimization problem. Especially in MPC for uncertain systems, on-line approach is often applied, the merits of which include enlarging the region of attraction and enhancing the optimality. In order to make the suboptimal arbitrarily close to the optimal, the infinite-horizon cost index is divided into two parts. The first part calculates the finite-horizon control moves by solving a finite-horizon optimization problem. The second part is formulated as an infinite-horizon min-max linear quadratic regulator based on polytopic inclusion of the time-varying dynamics in a neighborhood of the origin.
