Table 1 Summary of the PTC methods focused on weighting factor challenges.

Weighting factor removal by reference transformation^33,34

Higher computational burden as compared with conventional PTC and difficult to incorporate multiple control objectives³⁵

Weighting factor tuning based on coefficient of variation³⁶

Optimized weights are uncertain in this method and complex calculations are required to implement on hardware

Weighting factor tuning based on TOPSIS and NSGA-II methods³⁷

TOPSIS and NSGA-II algorithms require complex calculations leading to computational challenges¹²

Weighting factor removal by Ranking method³⁸

Ranking based techniques become unfeasible as number of control objectives increases³⁹

Tuning of weighting factor based on simple additive technique⁴⁰

Although technique is simple but not suitable for multiple control objectives¹¹

Weighting factor tuning based on current ripples⁴¹

Highly dependent on parameter estimation^8,42

Tuning of weighting factor based on error of control objectives⁴³

This method becomes challenging and complex when number of control objectives increases⁴⁴

Weighting factor tuning using Genetic Algorithm (GA)⁴⁵, Simulated Annealing (SA)⁴² or Gravitational Search Algorithm (GSA)⁴³, Artificial Neural Network⁴⁶, Ant colony based optimization⁴⁷

These algorithms are very complex and pose computational challenges⁴⁸

Weighting factor tuning based on algebraic/numerical techniques⁴⁹

Design complexity increases as slection of weighting factor increases⁵⁰

Weighting factor selection based on homogeneous cost functions^51,52,53

This technique is relatively efficient but unable to include multiple control objectives⁵⁴

Direct vector selection based techniques to remove weighting factors from cost function^55,56

Direct vector selection techniques provid lower computational burden and lower complexity , however cannot incorporate multiple control objecitve⁵⁷

Weighting factor elimination by using cascaded structure of FCS-MPC^58,59

The cascaded structure highly depended on proper selection of dealing cascaded structure⁶⁰