This paper presents a control system design for a type of time-varying nonlinear system. The control system comprises neuro-fuzzy system identifier, Luenberger observer, backstepping controller and variable structure controller. We use adaptive neuro-fuzzy inference system to identify the plant in real time without the need of underlying mathematical model. However, some knowledge about the plant structure and upper bounds is required. With the use of observer, the control system can be designed from plant output and input alone while plant states are assumed unmeasurable. Controller is designed based on backstepping scheme and uncertainties from the plant identification and state estimation processes are handled by variable structure controller. Under some important assumptions, the control system is proved to be able to track a smooth desired trajectory with uniformly ultimately bounded tracking error. A simulation based on one-link flexible-joint robot manipulator is provided.

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