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Significant interaction disturbances in surface vessel maneuvering and position tracking often require high precision controllers. In this paper we develop a coupled nonlinear two‐vessel tracking model for addressing the problem of underway replenishment. Next, using this model we develop an inverse optimal adaptive controller that guarantees disturbance rejection to exogenous disturbances while maintaining a desired separation between the two vessels.

~ Significant interaction disturbances exist while ships execute underway replenishment process, which can be characterized as position tracking problem and high precision controllers are required. In this paper we develop a coupled nonlinear two-vessel tracking model for addressing the problem of underway replenishment. Next, using this model we applied an inverse optimal adaptive controller that guarantees disturbance rejection to exogenous disturbances while maintaining a desired separation between the two vessels.

In this paper, we developed a dired adaptive control framework for MIMO nonlinear uncertain systems with matched exogenous disturbances, which are confined to admissible classes and characterized unmodeled dynamics and uncertain nonlineadties, We emphasize that the ' frameworks are Lyapunov-based and the proposed controllers address adaptive stabilization. Furthermore, A factored adaptive gain matrices are obtained when extended to linear systems.Finally, the proposed framework is applied to II numerical example for demonstration.