Programming-Based Optimal Learning Sliding Mode Control for Cooperative Dual Ship-Mounted Cranes Against Unmatched External Disturbances

When lifting and transporting large payloads in the marine environment, the dual ship-mounted crane system plays a very important role for cargos transportation, which exhibits strong load capacity and high flexibility. However, apart from the nonlinearity and underactuation characteristic, some unknown or uncertain unmatched wave disturbances may also cause positioning errors, which may induce various risks during the transportation process; besides, lots of existing methods ignore a part of the cooperative crane motions, and the control issue of dual ship-mounted crane system with five degrees of freedoms (5 DOF) is still open. In terms of the aforementioned problems, an adaptive dynamic programming (ADP)-based optimal learning sliding mode controller is proposed in this paper. Specifically, under the frame of adaptive dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation can be addressed. Then, based on the gradient attenuation algorithm, critic neural networks (NNs) are trained depending on the designed updating law and the approximate optimal learning controller can be obtained. Lyapunov techniques and Lasalle's invariance principle are used to guarantee asymptotic stability of the dual ship-mounted cranes system. Finally, a series of simulation results are depicted to show the effectiveness of the proposed optimal learning sliding mode controller. Note to Practitioners-In this paper, the control problem of a 5 DOF dual ship-mounted cranes system with unmatched wave disturbance is studied. Due to the complex nonlinear characteristics of the dual ship-mounted cranes and the need to consider the cooperative lifting and wave disturbances, the operation of the dual ship-mounted cranes are very challenging. Moreover, it brings more difficulties to the design of this kind of controller due to its nonlinear underactuated property. Existing control methods for dual ship-mounted cranes are based on linearized or oversimplified crane models, or require accurate model. To solve these kinds of problems, this paper proposes a new control approach for dual ship-mounted cranes suffering from unmatched wave disturbances to achieve satisfactory performance. The stability analysis of the closed-loop systems equilibrium point is implemented by Lyapunov techniques, implying that the accurate positioning and fast payload swings suppression against unmatched wave disturbances are achieved concurrently. In the future studies, we will apply the proposed control met