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This paper considers a new problem of control related to underwater vehicles. Due to the presence of a free fluid surface and to the vortex shedding of the vehicle lifting surfaces, the mathematical model is represented by an integral-differential equation. A new optimal control technique is investigated for this model, and its results compared with the use of a standard LQR method.

In this paper some models focusing on hydrodynamic and elasticforces arising during the impact of rigid and elastic systems on thewater surface are investigated. In particular, the supersoniccompressible stage of the impact is considered by modelling the slammingphenomenon through the Skalk–Feit acoustic approximation. The dynamicequations of the dropping system are coupled to those of the fluid and anonlinear fluid-solid interaction problem is stated. Generalrelationships between the body's shape, slamming force and body motionare determined. These equations are applied to the wedge water entrycases, and a closed-form expression for the maximum hydrodynamic forceis found. Moreover the theoretical correlation between the hydrodynamicforce and the body geometry allows us to control the inverse problem andthe shape associated to a constant slamming force is determined. Due to some simplifications allowed in the supersonic compressibleimpact, the results of the hydrodynamic analysis hold in closed form.This permits us to focus on the basic result of the paper addressed to asystematic correlation between hydrodynamic and elastic maximum forcesin terms of some characteristic dimensionless quantities involved influid-solid interaction. In particular, ‘critical conditions’corresponding to those hydorelastic parameters combinations areinvestigated, leading to severe elastic response of the impactingsystem.