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The integrated control deviation of mixed‐integer optimal control problems with vanishing constraints
Author(s) -
Bestehorn Felix,
Kirches Christian
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000022
Subject(s) - equidistant , rounding , mathematics , bounded function , integer (computer science) , mathematical optimization , grid , control (management) , optimal control , integer programming , computer science , mathematical analysis , geometry , artificial intelligence , programming language , operating system
Abstract Mixed‐integer optimal control problems (MIOCPs) are often solved using a decomposition approach, consisting of solving a partial outer convexified relaxed problem and using a rounding scheme to obtain a discrete‐valued control. We show that even in the presence of Vanishing Constraints (VCs) a binary control with linearly bounded integrated control deviation exists, if the grid is equidistant. We note that this control can be computed efficiently and that the bound is tight.