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This study deals with the problem of adaptive control for a class of non-linear systems with parameterisable time-varying actuator failures. An adaptive output-feedback actuator failure compensation scheme is proposed based on the backstepping technique and the Nussbaum gain approach. The assumption on the control gain signs is removed. The boundedness of all the closed-loop signals and the asymptotic output tracking are guaranteed in spite of the unknown actuator failures. Finally, an example is given to show the effectiveness of the proposed design method.