Set‐Membership‐Filtering‐Based Sliding Mode Control of Ship Positioning Systems in Polar Environments

ABSTRACT

To enhance ship dynamic positioning in polar environments under severe wind and ice loads, this paper proposes a discrete‐time sliding mode control strategy based on the set‐membership filtering. A discrete‐time nonlinear ship model is first established within a linear parameter‐varying framework to address modeling nonlinearities. Then, a recursive set‐membership filter is designed to provide robust interval state estimations of system states and disturbances under unknown‐but‐bounded noises. These estimation values are incorporated into an discrete‐time sliding mode control law for active uncertainty suppression. In addition, stability is established via difference inequality analysis, ensuring uniform ultimate boundedness. Finally, simulations results validate the effectiveness and precision of the proposed method under extreme conditions.