  For a class of uncertain systems, a non-overshooting sliding mode control is
presented to make them globally exponentially stable and without overshoot.
Even when the unknown stochastic disturbance exists, and the time-variant
reference trajectory is required, the strict non-overshooting stabilization is
still achieved. The control law design is based on a desired second-order
sliding mode (2-sliding mode), which successively includes two bounded-gain
subsystems. Non-overshooting stability requires that the system gains depend on
the initial values of system variables. In order to obtain the global
non-overshooting stability, the first subsystem with non-overshooting
reachability compresses the initial values of the second subsystem to a given
bounded range. By partitioning these initial values, the bounded system gains
are determined to satisfy the robust non-overshooting stability. In order to
reject the chattering in the controller output, a tanh-function-based sliding
mode is developed for the design of smoothed non-overshooting controller. The
proposed method is applied to a UAV trajectory tracking when the disturbances
and uncertainties exist. The control laws are designed to implement the
non-overshooting stabilization in position and attitude. Finally, the
effectiveness of the proposed method is demonstrated by the flying tests.
