Direct Data-Driven Tracking Control for Nonlinear Marine Vehicles

This paper addresses the tracking control problem of nonlinear fully-actuated/under-actuated marine vehicles (MVs) with unknown disturbances by establishing a novel direct data-driven control framework. We begin with fully-actuated MVs, characterized as a second-order strict-feedback system. This structure enables us to employ the recursive backstepping design method by introducing a virtual control law. To avoid identifying the complex kinetic model of MVs, we establish a data-based closed-loop representation for the error system of the tracking problem. Leveraging this representation and the backstepping technique, a data-driven tracking controller is derived by solving a semidefinite program with pre-collected noisy data. The proposed controller ensures the global uniform ultimate boundedness of solutions of the closed-loop system by approximately canceling the system's nonlinearity. Next, we tackle the more challenging under-actuated MVs that possess fewer control inputs than generalized coordinates, making direct nonlinearity cancellation inapplicable. To address this issue, we solve the tracking problem by stabilizing a new error system derived through a coordinate transformation. Notably, this new error system shares a similar structure with that of fully-actuated MVs but with a reduced dimension. This similarity enables us to seamlessly extend the results of fully-actuated MVs to under-actuated MVs. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed method.