Fractional order chattering-free robust adaptive backstepping control technique

Abstract

This paper proposes an observer-based fractional order robust adaptive backstepping control scheme for incommensurate fractional order systems with partial measurable state. The chattering phenomenon is carefully analyzed, and then a class of chattering-free controllers are proposed. To handle the time-varying disturbance, a robust adaptive control scheme is developed via the backstepping procedure. The method to generate the required fractional order differential signals online is provided. After designing the controller, the stability of the resulting closed-loop system is analyzed systematically. To highlight the efficiency of our findings, one illustrative example is provided at last.