Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach

This paper addresses the problem of tracking control and disturbance rejection for nonlinear fractional order systems. To this end, based on Takagi-Sugeno (T-S) fuzzy modeling approach and a fractional order modified repetitive controller, an output feedback strategy is constructed for a class of nonlinear fractional order systems. T-S fuzzy model represents an accurate model of nonlinear fractional order systems and simplifies the procedure of control system design. By introducing a novel Fuzzy Lyapunov Function (FLF), sufficient conditions are established in the framework of Linear Matrix Inequalities (LMIs) to ensure the stability of the closed-loop system. Based on the achieved conditions, it is shown that the external disturbance is attenuated and the output of the system tracks the periodic reference input with an ignorable error. Lastly, three examples including fractional order Chua's circuit, Lorenz-like and Chen systems are performed to show the efficiency of the method proposed in this paper. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a method to address the tracking control and disturbance rejection for nonlinear fractional order systems, utilizing T-S fuzzy modeling and a fractional order modified repetitive controller to construct an output feedback strategy. The stability of the closed-loop system is ensured by establishing sufficient conditions in the framework of LMIs with the introduction of FLF. The efficiency of the proposed method is demonstrated through three examples.