Linear Model Predictive Control via Multiparametric Programming

Abstract

IntroductionLinear systems with input, output, or state constraints are probably the most important class of systems in practice and the most studied as well. Although, a variety of control design methods have been developed for linear systems, it is widely accepted that stability and good performance for these systems, especially in the presence of constraints, is guaranteed with a nonlinear control law. The most popular nonlinear control approach for linear systems with constraints is model predictive control or simply MPC which has become the standard for constrained multivariable control problems in the process industries [24,25,35].MPC is an online constrained optimization method, based on the so-called receding horizon philosophy [24,25]. At each sampling instant, the measurements of the current output and/or state of the system are retrieved and an open-loop optimal control problem is solved over a finite time horizon to obtain the sequence of future control values. The first value of the sequence is then obtained and the procedure is repeated in the next sampling instant and over a shifted horizon, leading to a moving horizon policy. Since the objective function and the constraints of the open-loop optimal control problem can be set to express true performance objectives, the benefits of MPC are tremendous; optimality and constraints' satisfaction being obviously its main advantage.The application of MPC is, nevertheless, rather restricted, considering its profit potential, due to its online computational requirements which involve the repetitive solution of an optimization problem at regular time intervals. This limitation is in spite of the significant advances in the computational power of modern computers and in the area of online optimization over the past few years. Thus, it is fair to state that an efficient implementation of online optimization tools relies on a quick and repetitive online computation of optimal control actions. A way to avoid these repetitive online computations is by using multiparametric programming techniques to solve the optimization problem. With this approach, the control variables are obtained as an explicit function of the state variables and therefore the online Multi-Parametric Model-Based Control. Edited by E. Pistikopoulos, M. Georgiadis, and V. Dua

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