A Systematic Review on Function Approximation Technique (FAT) in Control Engineering

Abstract

Function Approximation Technique (FAT) is crucial in control systems in providing less complicated solutions and reducing computational difficulties due to its regressor-less approach. It is also essential for solving time-varying uncertainties in dynamics and external disturbances. A review of FAT is necessary to investigate the areas in which further research is needed and to provide guidance for future studies. This paper presents a systematic literature review on FAT in control systems. A comprehensive search of articles has been conducted in the well-established Scopus and Science Direct databases, targeting research published between 2022 and 2024. Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) framework has been adopted, resulting in 32 primary studies identified and analysed. The findings are categorized into three key themes: (1) applications of FAT-based controllers, (2) control strategies incorporating FAT and (3) advancements in the FAT formula. The findings reveal that FAT-based controllers are proven effective for various new systems, such as smart materials and multiagent systems. Robot manipulators continue to be the primary systems applied with FAT. The controllers incorporating FAT include adaptive, adaptive backstepping, adaptive sliding mode, robust adaptive, adaptive impedance with sliding mode controller and backstepping with compound learning control. The controller that adopts FAT representation the most in the selected papers is adaptive control. Modification in the FAT formula involves techniques that avoid the utilization of the basis function and the exploration of new basis functions that lead to lower computational efforts. Future research may explore the applications of FAT on other new systems, with different control strategies and alternative basis functions or methods that further simplify the technique. Future studies also may involve the investigations on eliminating the approximation errors in FAT, formulation of FAT for force control and hardware experimental tests to prove FAT based controllers’ practicality in real-time.