Adaptive actuator failure compensation for uncertain nonlinear fractional order strict feedback form systems

Abstract

In this paper, adaptive fractional control design is established for uncertain nonlinear fractional order strict feedback form systems with unknown actuator failures. The fractional actuator failure compensation problem is considered in the sense of two actuation shapes, and output matching conditions for these shapes are employed. By means of a fractional backstepping control method, two fractional adaptive state feedback control laws are designed to accomplish output tracking and to guarantee closed-loop stability in the presence of unknown actuator failures and unknown system parameters. A fractional order filter is proposed to avoid the problem of computational explosion of the backstepping design. The stability is proved via fractional order analysis method for the whole closed-loop system. Finally, simulation results for the control of fractional Chua’s circuit and fractional Genesio–Tesi systems demonstrate the effectiveness of the proposed actuator failure compensation method and output tracking property along with fast convergence of unknown parameters estimations.