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One is the non-harmonic disturbance coupled with system state and control input. The other one is an unexpected nonlinear signal described as a nonlinear function. The third one is white noise. An adaptive nonlinear disturbance observer (ANDO) is constructed to estimate non-harmonic disturbance. Based on which, a new adaptive nonlinear disturbance observer-based control (ANDOBC) strategy is developed such that the composite system is asymptotically bounded in mean square. 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