Discrete-Time Model Predictive Control

The focus of this chapter is on MPC of constrained dynamic systems, both linear and nonlin‐ ear, to illuminate the ability of MPC to handle constraints that makes it so attractive to in‐ dustry. We first give an overview of the origin of MPC and introduce the definitions, characteristics, mathematical formulation and properties underlying the MPC. Furthermore, MPC methods for linear or nonlinear systems are developed by assuming that the plant un‐ der control is described by a discrete-time one. Although continuous-time representation would be more natural, since the plant model is usually derived by resorting to first princi‐ ples equations, it results in a more difficult development of the MPC control law, since it in principle calls for the solution of a functional optimization problem. As a matter of fact, the performance index to be minimized is defined in a continuous-time setting and the overall optimization procedure is assumed to be continuously repeated after any vanishingly small sampling time, which often turns out to be a computationally intractable task. On the con‐ trary, MPC algorithms based on discrete-time system representation are computationally simpler. The system to be controlled which usually described, or approximated by an ordi‐ nary differential equation is usually modeled by a difference equation in the MPC literature since the control is normally piecewise constant. Hence, we concentrate our attention from now onwards on results related to discrete-time systems.