Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output

Abstract

This brief addresses the trajectory tracking control problem of a fully actuated surface vessel subjected to asymmetrically constrained input and output. The controller design process is based on the backstepping technique. An asymmetric time-varying barrier Lyapunov function is proposed to address the output constraint. To overcome the difficulty of nondifferentiable input saturation, a smooth hyperbolic tangent function is employed to approximate the asymmetric saturation function. A Nussbaum function is introduced to compensate for the saturation approximation and ensure the system stability. The command filters and auxiliary systems are integrated with the control law to avoid the complicated calculation of the derivative of the virtual control in backstepping. In addition, the bounds of uncertainties and disturbances are estimated and compensated with an adaptive algorithm. With the proposed control, the constraints will never be violated during operation, and all system states are bounded. Simulation results and comparisons with standard method illustrate the effectiveness and advantages of the proposed controller.