Determination of attainable regions in ship maneuvers: an application of differential inclusions to the modeling of ship dynamics

A commonly used mathematical tool in vehicle dynamics simulation is the ordinary differential equation. However, in some situations, these equations may not be sufficient to solve problems. For robust flight, surface ship or submarine control design, safety assessment, missile and aircraft guidance, the influence of disturbances, and differential games of pursuit–evasion, more versatile tools are needed. The differential inclusion (DI) is a generalization of a differential equation that can be extremely useful. The solution of a DI is not just a model trajectory or a set of trajectories obtained by a randomization of the original problem. The solution is a reachable set, and it is a deterministic object. A differential inclusion solver and its application to vessel movement are described. Compared to previous publications on the DI solver, the new feature is an implementation of the fuzzy sets technique to improve the resulting images. It is pointed out that the reachable sets cannot be assessed properly while treating the uncertain variables as random. The application of the DI solver can give a proper view of the regions in the state space where all the possible model trajectories belong.