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Supercavitating vehicles can achieve very high speed but also pose technical challenges in system stability, maneuvering, and control. Compared to a fully-wetted vehicle for which substantial lift is generated due to vortex shedding off the hull, a supercavitating vehicle is enveloped by gas surface (cavity) and thus the lift is provided by control surface deflections of the cavitator and fins, as well as planing force between the vehicle and the cavity. The nonlinearity in modeling of the cavitator, fins, and especially in modeling of the planing force makes the control design more difficult. In this paper, we investigate several nonlinear control design approaches such as sliding-mode control and quasi linear-parameter-varying control for the dive-plane dynamics of a supercavitating vehicle model. The stability and robustness of the final designs are analyzed. Since only a partial set of state variables are measurable, a high-gain observer is also designed to estimate state variables that are not directly available for feedback. Considering the physical limits of deflection angles of control surfaces of the cavitator and fins, we design a saturation compensator and activate it when needed. Then simulation results are presented for the (partial) output feedback controllers, which are combination of state-feedback nonlinear controllers and the high-gain observer.