What is it about?

A decisive feature of the turnpike pheomenon is that far away from the boundary points of the time interval, the solution of the dynamic problem is close to the solution of the corresponding static problem. The notion 'the turnpike phenomenone with interior decay' refers to this situation. In this paper we show that under a cheap control condition and a strict dissipativity assumption this turnpike property holds.

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Why is it important?

The turnpike property allows to decompose optimal control processes into three phases: An initial phase, a terminal phase and an intermediate phase between the first two phases. With increasing time interval, only the length of the intermediate phase increases. This is an important insight that helps to understand the nature of the optimal control process. Moreover, this structural information can be used to gain computational efficiency in the appproximation of the optimal controls.


It is important to apply the general studies of the turnpike property to specific numerical computations.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

Read the Original

This page is a summary of: On the turnpike property with interior decay for optimal control problems, Mathematics of Control Signals and Systems, March 2021, Springer Science + Business Media,
DOI: 10.1007/s00498-021-00280-4.
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