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Properties of time transformed mixed-integer optimal control problems

Sebastian Sager(sager***at***ovgu.de)
Manuel Tetschke(manuel.tetschke***at***ovgu.de)

Abstract: A time transformation is an ubiquitous tool in theoretical sciences, especially in physics. It can also be used to transform switched optimal control problems into control problems with a fixed switching order and purely continuous decisions. This approach is known either as enhanced time transformation, as time-scaling, or as switching time optimization for mixed-integer optimal control. Recently, several extensions and algorithmic improvements have been proposed. We use an alternative transformation, the partial outer convexification, as a tool to analyze properties of time transformed problems. In particular we show that and why the nonconvexity of the transformed problem may become an issue. Two numerical studies illustrate this and show that an initialization based on a partial outer convexification is beneficial.

Keywords: Mixed-integer optimal control, MINLP, time transformation, relaxation

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Global Optimization (Theory )

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Submitted to Mathematical Programming B

Download: [PDF]

Entry Submitted: 03/27/2020
Entry Accepted: 03/27/2020
Entry Last Modified: 03/27/2020

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