Time optimal control with a class of dependent input constraints

This paper focuses on the new properties of time optimal control problems with a class of dependent input constraints. Based on such constraints, both of the theoretical analysis and the geometry interpretations are investigated for time optimal control problems. According to these input constraints, a special kind of bang-bang control called dynamic single-input control is introduced, which has a form that only a single input channel works at its extreme value while the other channels are unused and the working channel may hop among different input channels during the entire optimal period. Moreover, through the geometric perspective, it is illustrated that the dependent input constraints will guarantee a more efficient time optimal control than the one with standard input constraints. Finally, a numerical example is employed to demonstrate the results in the paper.