# Performance Assessment of Predictive Control--A Survey
## 4 MPC Performance Assessment
### Data-Driven Approaches  
The data-driven approach is less frequently observed in the literature. The explanation is quite simple. As there is no model, it does not depend on the loop control algorithm. Thereby, any existing model-free approach might be used. The interest shifts towards the interpretation of the results. Consecutively, any approach using step responses (overshoot and settling time), integral indexes (MSE and IAE), signals correlation, statistical approaches (standard deviation, histogram broadness, distortion coefficients, and tail index), information entropies, persistence, and fractal measure may be equally used.  
The first simple assessment approaches have utilized comparison of time trends [149], which is in fact the first thing being done in any practical assessment. Actually, it must be done. A statistical method was also developed by [PERSON] and [PERSON] [150], further followed by [PERSON] and [PERSON] [151], who focused on the derivation of simple and intuitive charts to support plant operators.  
[PERSON] et al. [152] proposed applying sensitivity function and integral squared error as performance evaluation criteria in the frequency and time domain respectively, to quantitatively analyze single prediction strategy.  
Similar to the model-driven approaches, predictive structures have been assessed in different application configurations, i.e., as a main regulatory controller or in the supervisory level over PID control loops [153].  
An interesting approach using novel, multivariate statistical technology called Slow Feature Analysis (SFA) has been proposed to separate temporal slow features from process variables. It was firstly used for diagnostics, and then extended to the MPC assessment task [154], lately followed by further modifications [155; 156]. The approach enables monitoring both steady-state and dynamic responses.  
Non-Gaussian statistical [157] and fractal [158] methodologies have been investigated for the GPC predictive control algorithm. Linear [159] and nonlinear [160] DMC predictive control have been assessed using integral, statistical, information, and fractal measures. This research has shown that dispersion coefficients of the non-Gaussian \(\alpha\)-stable distribution are robust against industrial disturbances and they allow measuring control quality and to detect wrong MPC design. Similar effects can be obtained with the robust statistics approach. Robust scale estimators, such as Mean Absolute Deviation (MAD), Mean Absolute Deviation Around Median (MADAM), Least Median Square (LMS), or m-estimator using logistic \(\psi\) function deliver further alternatives. In addition, information technology brings forward the possibility to use entropy measures [160].  
Furthermore, fractional-order dynamics increases possible set of robust and non-Gaussian indicators [107; 108]. [PERSON] et al. [161; 162] proposed to evaluate MPC performance and capture the fluctuation of the process variables with a performance index based on Mahalanobis distance. This distance is used to construct a support vector machine classifier that allows recognizing common quality degradation schemes and determining the root cause of bad performance.