Control elimination of time optimal bang-bang control with a class of input constraints

This paper focus on the time optimal control problems with a class of dependent input constraints while all the input channels are dependent on the others. Based on such a class of constraints, a concept of control elimination is introduced, in which the optimal time will not increase when the idle and redundant input channels have been removed. Then, after examining the normality, we prove the existence theorem for control elimination. Finally, several numerical examples are given to demonstrate the main result of the paper, and the application to control allocation.