Linear matrix inequalities-based adaptive time-delayed sliding mode control for ships considering ship-bank interaction effect and shallow water effect

To deal with the uncertain system models with less computational cost, expertise knowledge and parameter tuning, a linear matrix inequalities (LMI)-based adaptive time-delayed sliding mode control algorithm is proposed. It is used for ships berthing or sailing near the bank or the pier of a bridge considering ship-bank interaction effect and shallow water effect. The closed-loop system is proved to be uniform ultimate bounded based on the Lyapunov-Razumikhin function in terms of LMI. The switching function is designed to make the system robust to uncertainties and external disturbances and avoid chattering. The trajectory of the system space is contractive and asymptotically tends to the desired position and attitude. The influence of different control parameters on the control effect are compared and analyzed. The results show that when the control coefficients are small, the overshoot of the system is small. The adjustment time of the system is long. When the control coefficients are large, the overshoot of the system is obvious. The adjustment time of the system is shortened. Influence analysis of different input time delays show that when the input delay is long, it takes longer time for the system to reach its desired position with higher overshoot. When the input delay is short, it takes shorter time for the system to reach its desired position with lower overshoot.