MPC Formulation of GLC

During the last decade, there has been a growing interest in developing nonlinear model-based control methods. This interest has led to substantial progress mainly within the two frameworks of model predictive control (MPC) and differential geometric control. MPC is an optimization-based control methodology which explicitly accounts for process constraints and in general leads to a controller without an analytical form (see Muske and Rawlings (1993) for a recent thorough review of MPC). However, differential geometric control is a feedback linearization-based control methodology which leads to a controller with an analytical form, as in globally linearizing control (GLC) (Soroush and Kravaris, 1992). An objective of this note is to show that not only are these two apparently different control methodologies closely related, but also in some cases they lead to identical controllers. In particular, this note establishes that the input-output linearizing control laws derived in our previous article (Soroush and Kravaris, 1996) are indeed model predictive control laws. The specific objectives of this work are: To derive a nonlinear MPC law with the shortest useful prediction horizon for each controlled output. To prove that the derived model predictive controller is exactly the reduced-order error-feedback globally linearizing controller derived in (Soroush and Kravaris, 1996). Following the description of the scope of this work, the shortest-horizon MPC law is derived and shown to be exactly a reduced-order error-feedback globally linearizing controller. The nonlinear MPC law is then applied to unconstrained linear processes, and the resulting linear controller is shown to be exactly a model algorithmic controller (Mehra and Rouhani, 1980) and an internal model controller (Garcia and Morari, 1985).