  A ship steering control is designed for a nonlinear maneuvering model whose
rudder manipulation is constrained in both magnitude and rate. In our method,
the tracking problem of the target heading angle with input constraints is
converted into the tracking problem for a strict-feedback system without any
input constraints. To derive this system, hyperbolic tangent ($\tanh$) function
and auxiliary variables are introduced to deal with the input constraints.
Furthermore, using the feature of the derivative of $\tanh$ function, auxiliary
systems are successfully derived in the strict-feedback form. The backstepping
method is utilized to construct the feedback control law for the resulting
cascade system. The proposed steering control is verified in numerical
experiments, and the result shows that the tracking of the target heading angle
is successful using the proposed control law.
