Assessment and Future Directions of Nonlinear Model Predictive ...

2 E.F. Camacho and C. Bordonsin the state space or input-output domain, is usually preferred as being moreintuitive and requiring less aprioriinformation for its identification.Another line of work arose independently around adaptive control ideas, developingstrategies essentially for monovariable processes formulated with inputoutputmodels. Some examples of these strategies are Extended Prediction SelfAdaptive Control (epsac) by De Keyser and Van Cuawenberghe [20] or GeneralizedPredictive Control (gpc) developed by Clarke et al. in 1987 [9].mpc is considered to be a mature technique for linear and rather slow systemslike the ones usually encountered in the process industry. More complexsystems, such as nonlinear, hybrid, or very fast processes, were considered beyondthe realm of mpc. During the last few years some impressive results havebeen produced in these fields. Applications of mpc to nonlinear and to hybridprocesses have also appeared in the literature. The majority of applications (seesurveys by Qin and Badgwell [35] [36]) are in the area of refining, one of the originalapplication fields of mpc, where it has a solid background. An importantnumber of applications can be found in petrochemicals and chemicals. Althoughmpc technology has not yet penetrated deeply into areas where process nonlinearitiesare strong and frequent changes in operation conditions occur, thenumber of nonlinear mpc applications is clearly increasing.In general, industrial processes are nonlinear, but many mpc applications arebased on the use of linear models. There are two main reasons for this: on onehand, the identification of a linear model based on process data is relatively easyand, on the other hand, linear models provide good results when the plant isoperating in the neighbourhood of the operating point. Besides, the use of alinear model together with a quadratic objective function gives rise to a convexproblem whose solution is well studied with many commercial products available.Notice that mpc of a linear plant with linear constraints gives rise to anonlinear controller, and that this combination of linear dynamics and linearconstraints has influenced on the commercial success of mpc. However, the termNonlinear mpc is used for Predictive Controllers that make use of a nonlineardynamic model (and therefore nonlinear constraints) and gives rise to the extracomplexity.In many situations the operation of the process requires frequent changesfrom one operation point to another and, therefore, a nonlinear model must beemployed. The use of Nonlinear Model Predictive Control (nmpc) is justified inthose areas where process nonlinearities are strong and market demands requirefrequent changes in operation regimes. Although the number of applications ofnmpc is still limited (see [3], [36]), its potential is really great and mpc usingnonlinear models is likely to become more common as users demand higher performanceand new software tools make nonlinear models more readily available.From a theoretical point of view using a nonlinear model changes the controlproblemfromaconvexqp to a non-convex Non-Linear Program (nlp), thesolution of which is much more difficult. There is no guarantee, for example,that the global optimum can be found.