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One of the most important issues, which high-speed underwater vehicles (HSUV) deal with, is the so-called planing force. The dynamic of HSUV includes two separate phases called planing phase and non-planing phase. Ideally, in perfect flight, the vehicle should fly within the cavity walls. However, in practice, the vehicle impacts on the cavity boundaries due to disturbances. The magnitude of the planing force is large and has a strong effect on dynamics of HSUV. However, planing force modeling is often too simple and therefore inaccurate, due to the nonlinear interaction among the solid, liquid, and gaseous phases, which is not well understood yet. Consequently, planing force identification is of great importance and should be studied in details. The present paper discusses the identification of the planing force in HSUV. For this purpose, the equations of motion are developed for the HSUV in the planing phase while the tail and the body end impact on the cavity wall. Then, a robust hybrid switching control approach is employed to deal with the highly nonlinear behavior of the underwater vehicle as it is influenced by the liquid-gas boundary interactions. An on-line planing force identification based on Lyapunov function is considered within designing controller procedure, thus the stability of the system is guaranteed. Lateral and longitudinal planing force identification are achieved and discussed. Compared to the proportional-integral-derivative control scheme, the hybrid control scheme seems to increase the stabilization of HSUV, which is useful in avoiding unsteady changes of cavity shape.

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A new general robust fuzzy approach was presented to control the position and the attitude of unmanned flying vehicles (UFVs). Control of these vehicles was challenging due to their nonlinear underactuated behaviors. The proposed control system combined great advantages of generalized indirect adaptive sliding mode control (IASMC) and fuzzy control for the UFVs. An on-line adaptive tuning algorithm based on Lyapunov function and Barbalat lemma was designed, thus the stability of the system can be guaranteed. The chattering phenomenon in the sliding mode control was reduced and the steady error was also alleviated. The numerical results, for an underactuated quadcopter and a high speed underwater vehicle as case studies, indicate that the presented adaptive design of fuzzy sliding mode controller performs robustly in the presence of sensor noise and external disturbances. In addition, online unknown parameter estimation of the UFVs, such as ground effect and planing force especially in the cases with the Gaussian sensor noise with zero mean and standard deviation of 0.5 m and 0.1 rad and external disturbances with amplitude of 0.1 m/s 2 and frequency of 0.2 Hz, is one of the advantages of this method. These estimated parameters are then used in the controller to improve the trajectory tracking performance.

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