An Introduction to Nonlinear Model Predictive Control

While linear model predictive control is popular since the 70s of the past century, the 90s have witnessed a steadily increasing attention from control theoretists as well as control practitioners in the area of nonlinear model predictive control (NMPC). The practical interest is driven by the fact that today’s processes need to be operated under tighter performance specifications. At the same time more and more constraints, stemming for example from environmental and safety considerations, need to be satisfied. Often these demands can only be met when process nonlinearities and constraints are explicitly considered in the controller. Nonlinear predictive control, the extension of well established linear predictive control to the nonlinear world, appears to be a well suited approach for this kind of problems. In this note the basic principle of NMPC is reviewed, the key advantages/disadvantages of NMPC are outlined and some of the theoretical, computational, and implementational aspects of NMPC are discussed. Furthermore, some of the currently open questions in the area of NMPC are outlined. 1 Principles, Mathematical Formulation and Properties of Nonlinear Model Predictive Control Model predictive control (MPC), also referred to as moving horizon control or receding horizon control, has become an attractive feedback strategy, especially for linear processes. Linear MPC refers to a family of MPC schemes in which linear models are used to predict the system dynamics, even though the dynamics of the closed-loop system is nonlinear due to the presence of constraints. Linear MPC approaches have found successful applications, especially in the process industries. A good overview of industrial linear MPC techniques can be found in [64, 65], where more than 2200 applications in a very wide range from chemicals to aerospace industries are summarized. By now, linear MPC theory is quite mature. Important issues such as online computation, the interplay between modeling/identification and control and system theoretic issues like stability are well addressed [41, 52, 58]. Many systems are, however, in general inherently nonlinear. This, together with higher product quality specifications and increasing productivity demands, tighter environmental regulations and demanding economical considerations in the process industry require to operate systems closer to the boundary of the admissible operating region. In these cases, linear models are often inadequate to describe the process dynamics and nonlinear models have to be used. This motivates the use of nonlinear model predictive control. This paper focuses on the application of model predictive control techniques to nonlinear systems. It provides a review of the main principles underlying NMPC and outlines the key advantages/disadvantages of NMPC and some of the theoretical, computational, and implementational aspects. Note, however, that it is not intended as a complete review of existing NMPC techniques. Instead we refer to the following list for some excellent reviews [4, 16, 22, 52, 58, 68]. In Section 1.1 and Section 1.2 the basic underlying concept of NMPC is introduced. In Section 2 some of the system theoretical aspects of NMPC are presented. After an outline of NMPC schemes that achieve stability one particular NMPC formulation, namely quasi-infinite horizon NMPC (QIH-NMPC) is outlined to exemplify the basic ideas to achieve stability. This approach allows a (computationally) efficient formulation of NMPC while guaranteeing stability and performance of the closed-loop. Besides the basic question of the stability of the closed-loop, questions such as robust formulations of NMPC and some remarks on the performance of the closed-loop are given in Section 2.3 and Section 2.2. Section 2.4 gives some remarks on the output-feedback problem in connection with NMPC. After a short review of existing approaches one