The integrated control deviation of mixed‐integer optimal control problems with vanishing constraints

Abstract Mixed‐integer optimal control problems (MIOCPs) are often solved using a decomposition approach, consisting of solving partial outer convexified relaxed problem and rounding scheme to obtain discrete‐valued control. We show that even in the presence Vanishing Constraints (VCs) binary with linearly bounded integrated deviation exists, if grid is equidistant. note this can be computed efficiently bound tight.