A cascade system of an autonomous underwater vehicle is considered. It consists of the nonlinear equation of motion and the equations of actuator dynamics. In the motion equation, unmatched uncertainties are taken into account, including the modeling errors and the bounded disturbances. The modeling errors result from the parameter errors, the ignored high-order modes and unmodelled dynamics. The bounded disturbances refer to environment forces or unknown random disturbances. To obtain accurate manoeuvring of the underactuated system, a hybrid robust controller is proposed by using backstepping Lyapunov functions. A two-layer feedforward neural-network is applied to compensate the modeling errors and the derivatives of desired control inputs, while the H control strategy is used to achieve the L2-gain performance with respect to the bounded disturbances. The on-line tuning algorithms of the neural-network weights are given. The uniformly ultimately bounded stabilities of the tracking errors and the neural-network weights errors are analyzed. Moreover, selection of the gains in controller is recommended by analysis of the upper boundedness of errors. Simulation results have demonstrated the validity of the controller proposed.

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