The effect of an event-triggered controller on non-strict feedback system based on the single input interval type-2 fuzzy method

Abstract

Non-Strict Feedback (NSF) physical systems are broader than Strict-Feedback (SF) systems. The system state variables depend on their system functions, unlike SF systems that the system variables do not depend on their system function. Consequently, NSF physical systems are challenging to control. To address this control challenge in NSF physical systems, this research proposed an Event-Triggered (ET) adaptive backstepping control method based on Single Input Interval Type-2 Fuzzy (SIIT-2F) for NSF system with input delay. The effect of the method is examined on a third order system using transient and steady state performance as a metric. The ET mechanism prompts due to violation of a predefined condition (mismatch between the actuator and the controller), uncertainty of the system dynamics was handled by the Radial Basis Function Neural Network (RBFNN). The input delay was handled by a developed auxiliary system, and the SIIT-2F was used to minimize error between state variables and auxiliary states of the adaptive backstepping controller. The results of this work were compared with adaptive neural control for NSF method. The method has an average percentage performance improvement of23% peak overshoot for state variables; and 47% for adaptive variables, the average performance improvement for the absolute peak undershoot are 50%, and 60% respectively for the state and auxiliary variables. In addition, the settling time average performance improvement is 11%, 21%, and 10% for state, auxiliary, and adaptive variables, respectively. The results of this study underline that the ET based SIIT-2F controller improved the performance of NSF systems compared to the adaptive neural control method.