Global robust adaptive path-tracking control of underactuated ships under stochastic disturbances

This paper presents a design of new controllers that force underactuated ships under both deterministic and stochastic sea loads to globally track a reference path. First, the loads are decomposed to a deterministic part treated as unknown constants, and a time-varying part considered as stochastic disturbances with unknown time-varying covariances. Second, the path-tracking errors are represented in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov׳s direct methods. Weak and strong nonlinear Lyapunov functions are introduced, and the path-parameter is used as an additional control input to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule. Estimate of the deterministic disturbances and upper covariances of the stochastic disturbances is incorporated in the control design. The effectiveness of the proposed results is illustrated through simulations.