Nonlinear minimum-time control with pre- and post-actuation

This article studies the time-optimal output transition problem to change the system output, from an initial value y(t)=y¯ (for all time t≤0) to a final value y(t)=y¯ (for all time t≥T), for invertible nonlinear systems. The main contribution of the article is to show that the use of pre- and post-actuation input outside the transition interval IT=[0,T]IT=[0,T] can reduce the transition time TT beyond the standard bang–bang-type inputs for optimal state transition. The advantage of using pre- and post-actuation is demonstrated with an illustrative nonlinear example.