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Underactuated mechatronic systems are widely used in industrial production, where the control efforts and operation accuracy are both important aspects of performance evaluations. Hence, how to realize effective motion control, while reducing control efforts as much as possible, becomes an open problem for underactuated systems. Although some open loop approaches (e.g., trajectory planning) take energy optimization into account, they need linearization/approximation manipulations and exhibit weak robustness, which is prone to degrading practical control performance. To this end, this article proposes an adaptive tracking controller for uncertain multi-input-multi- output (MIMO) underactuated mechatronic systems, to fulfill accurate positioning/tracking control with saturated inputs and reduce control efforts as well. Particularly, by elaborately developing an auxiliary compensation term and a robust term, the proposed controller ensures asymptotic convergence of both actuated and unactuated variables. Meanwhile, the modified performance index function is approximated online and introduced into the Lyapunov function candidate to make the stability analysis process more concise. To the best of our knowledge, without the need of offline computation and the persistence of excitation (PE) condition, this article presents the first adaptive optimal controller to simultaneously achieve error elimination, control effort optimization, and actuator constraints for a class of underactuated systems. Finally, strict theoretical analysis and experimental validations show the effectiveness and robustness of the suggested controller.

Underactuated systems are widely used in practice. Due to actuator saturation and transient performance requirements, it is necessary to keep the control inputs and system states within safe limits. However, with fewer control inputs, the state constraints, especially for unactuated states, are usually difficult to guarantee. Model predictive control (MPC), as a method that can handle constraints naturally, unfortunately, still struggles to deal with unactuated variable constraints directly. To this end, this article proposes a general MPC algorithm for a class of underactuated systems. First, an MPC method considering actuator saturation constraints is designed, based on which, different velocity constraint-related matrices are constructed to convert both actuated and unactuated velocity constraints into control input constraints. Then, by delicately analyzing the coupling relationship between actuated and unactuated variables, the displacement/angle constraints of unactuated variables are theoretically ensured. To our best knowledge, it is the first MPC approach designed for a class of underactuated systems with both actuated and unactuated state constraints as well as actuator saturation. Finally, the proposed MPC approach is applied to two typical underactuated systems, i.e., tower cranes and boom cranes, and a series of experiments are investigated to verify the effectiveness and superiority of this approach.

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 method to industrial dual ship-mounted cranes systems to improve their working safety and efficiency.