Continuous Fractional-Order Sliding PI Control for Nonlinear Systems Subject to Non-Differentiable Disturbances

Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Holder type, a continuous and chattering-free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differintegral operators to show that a sliding mode is induced, and sustained, in finite-time, to guarantee asymptotic tracking. The closed-loop system achieves exact rejection of Holder disturbances even in case of uncertain flow, but assuming certain knowledge of the input matrix. Furthermore, it is shown that our methodology generalizes continuous high-oder sliding mode schemes by using an integral action of fractional-order. A representative simulation study is discussed to show the feasibility of the proposal.