Connection between singular arcs in optimal control using bridges. Physical occurence and Mathematical model

Abstract

In the time minimal control problem, singular arcs are omnipresent to determine the optimal solutions and this leads to the well known turnpike phenomenon [1]. Very recently, this connection between singular arcs using a bang arc was shown to be relevant to saturate a single spin in Magnetic Resonance Imaging. Based on this example we propose a mathematical model to analyze such connection, which is called a bridge. This is applied to compute bridges in the optimization of chemical reaction networks using temperature control.