# Performance Assessment of Predictive Control--A Survey
## 2 Model Predictive Control
### General MPC Rule
Such a simplification enables embedding DMC or GPC inside of a DCS system [42]. The main difference between the DMC and GPC lies in the type of the model used. DMC was first presented by [PERSON] and [PERSON] at AIChE meeting in 1979 [18] and at the Automatic Control Conference in 1980 [43]. Almost simultaneously it was applied to catalytic cracking unit and the algorithm was modified to handle nonlinearities and constraints [44]. The algorithm went through several modifications, as for instance Quadratic Dynamic Matrix Control (QDMC) [45] using quadratic programming for solving constrained open-loop optimal control task, where the system is linear, the objective function is quadratic, and the constraints are defined by linear inequalities or the numerically efficient version used in the embedded environment [46]. Discrete-time step response model of the controlled process used for prediction calculation, i.e., finding the values of \(\hat{y}_{m}(k+p|k)\), is the main DMC algorithm feature. Although it is limited only to stable processes. Its main advantage is the step-response process model, which may be easily obtained during practice. Since the step-response model is linear in terms of the manipulated variables, minimization of the general MPC cost-function in Equation (3) leads to computationally simple quadratic optimization task. When there are no constraints imposed on the process variables, the solution may be evaluated analytically. The unconstrained MPC optimization may be projected onto the admissible set determined by the constraints [11]. Generalized Predictive Control was introduced by [PERSON] in 1987 [19; 20] with several further extensions (e.g., [47; 48]). Regression-type discrete difference equation are used as a model in the GPC algorithm. Such model may be named as Auto-Regressive Integrated Moving Average with auXiliary Input (ARIMAX) or Controlled Auto-Regressive Integrated Moving Average (CARIMA) [11]. It is often assumed that the process is affected by an integrated white noise that simplifies the further utilized process model. It is also important to note that, according to the GPC prediction scheme, future CV predictions are simple, linear functions of the calculated decision vector and utilize free trajectory, which depends only on the past. Thereby, general MPC optimization problem can be modified accordingly. As the prediction relation is linear in terms of the obtained decision vector, the resulting optimization problem is defined as a Quadratic Programming (QP) type, which means that the cost-function is quadratic and all constraints are linear. The above MPC configurations require a priori knowledge about the process, which must be somehow derived, for instance using the first principle modeling [49; 50] or experimental empirical identification such as artificial neural networks [51; 52], Hammerstein-Wiener configurations [41; 53], fuzzy [54; 55], and neuro-fuzzy [56; 57] or Gaussian processes [58; 59]. Apart from the majority of MPC configurations, which use internal process model, there are techniques that do not require explicit model definition. Model free configurations include, among others, machine learning techniques, such as regression trees [60], random forests [61], or reinforcement learning [62]. Although both GPC and DMC predictive algorithms are well established within the industry and there are many reported successful implementations over last 40 years, their practical design, tuning, and performance assessment is still a challenging task [63; 64].