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 (for all time ) to a final value (for all time ), 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 I_T=0,T] can reduce the transition time T 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.