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arXiv · 1509.07315

On Turnpike and Dissipativity Properties of Continuous-Time Optimal Control Problems

Timm Faulwasser·Milan Korda·Colin N. Jones·Dominique Bonvin
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Abstract

This paper investigates the relations between three different properties, which are of importance in optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnpike property. We show in a continuous-time setting that if along optimal trajectories a strict dissipation inequality is satisfied, then this implies optimal operation at this steady state and the existence of a turnpike at the same steady state. Finally, we establish novel converse turnpike results, i.e., we show that the existence of a turnpike at a steady state implies optimal operation at this steady state and dissipativity with respect to this steady state. We draw upon a numerical example to illustrate our findings.

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Timm Faulwasser, Milan Korda, Colin N. Jones, Dominique Bonvin. 2015-09-24. On Turnpike and Dissipativity Properties of Continuous-Time Optimal Control Problems. https://doi.org/10.1016/j.automatica.2017.03.012

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