Robust adaptive backstepping control design for a supercavitating vehicle model

In this paper, robust adaptive backstepping control is applied for a supercavitating vehicle model to account for the unknown slope in the fin force of the vehicle model. In the benchmark supercavitating-vehicle model, which is widely used for control designs in the literature, the fin force was modeled as a linear function with respect to the fin angle of attack, and the slope of the fin force was considered to be a known constant for a fixed cavitation number. However, more realistic modeling for fin force shows that the fin force slope is a function of the fin deflection angle, fin sweepback angle and fin immersion. Additionally, noting that the cavity shape at the transom region determines immersion of the fins, the fin immersion and thus the slope of the fin force will also be impacted by the so-called memory effect due to cavity-vehicle interaction. In this paper, we consider the fin effectiveness parameter relative to the cavitator, which is used to compute the slope of the fin force, to be an unknown parameter. Then we design a parameter estimation law for this fin effectiveness parameter and an adaptive backstepping controller to stabilize the supercavitating vehicle model. We prove the boundedness of all the signals and convergence of vehicle state variables via Lyapunov stability theory. In addition, if the bound of the fin effectiveness parameter is known, a projection of the parameter adaptive law can be used and the resulting controller implementation will maintain the boundedness and convergence properties.