Resilient event-triggered practically predefined-time heading control of ships with delay of steering gear and false-data-injection attacks

The presence of time delays prevents the controller from responding to disturbances promptly, resulting in excessive overshoot and prolonged settling times. Moreover, traditional predefined-time stability theorems are not directly applicable to systems with operational delays. To address this, a practical predefined-time tracking control strategy is designed under input delays and false data injection attacks. By employing virtual controllers to compensate for unknown gains caused by such attacks, the adverse effects are mitigated effectively and rapidly. Considering the time delay in the steering gear, an adaptive strategy is introduced to adjust the controller parameters online, enhancing the system’s adaptability to varying delays. Furthermore, a predefined-time convergent observer is developed to handle system uncertainty, effectively eliminating the impact of attacks and external disturbances. The proposed method is validated using ships. Additionally, the impact of delays on the system in multiple scenarios is discussed. The proposed approach effectively suppresses the effects of both attacks and delays. Compared to traditional control methods such as fixed-time control and continuous control, the results demonstrate a significant reduction in computational cost.