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This paper investigates the formation keeping problem of heterogeneous ships with underactuated inputs, uncertain dynamics, and environmental disturbances. The control objective is to make the heterogeneous followers keep the desired formation while tracking a leader. To solve the problem effectively, a novel virtual leader–follower formation scheme considering the ship heterogeneity is proposed by utilizing the backstepping method, adaptive neural network, and adaptive control law. The stability of the formation control system is proved based on Lyapunov's direct method where all tracking errors are guaranteed to be uniformly ultimately bounded. Finally, simulations and comparisons are conducted to verify the effectiveness of the proposed control law., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Transport Engineering and Logistics

It is of significant importance to optimize the energy consumption of ships in order to improve economy and reduce CO2 emissions. However, the energy use of ships is affected by a series of navigational environmental parameters, which have certain spatial and temporal differences and variability. Therefore, the dynamic collaborative optimization method of sailing route and speed, which fully considers the spatial and temporal distribution characteristics of those factors, is of great importance. In this paper, the spatial and temporal distribution characteristics of the environmental factors and their related ship energy consumption profiles are first analyzed. Subsequently, a ship energy consumption model considering various environmental factors is established to realize the prediction of energy use of ships within the navigation region. Then, a novel dynamic collaborative optimization algorithm, which adopts the Model Predictive Control (MPC) strategy and swarm intelligence algorithm, is proposed, to further improve the ship's energy consumption optimization. Finally, a case study is conducted to demonstrate the effectiveness of the proposed method. The results show that the newly developed dynamic collaborative optimization method, which fully considers the continuously time-varying characteristics of environmental and operational parameters, could effectively reduce the energy consumption in comparison to the original operational mode. In addition, the adoption of the MPC strategy produces better performance results compared to the optimization method without the MPC strategy., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Transport Engineering and Logistics