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Economic NMPC for averaged infinite horizon problems with periodic approximations

Feedback control for averaged infinite horizon problems is a challenging task because the optimal way to operate such systems often exhibits a time-varying behavior, i.e. it cannot be represented as a steady state. We present a controller that is based on the excellent approximation properties of pe...

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Main Authors: Gutekunst, Jürgen (Author) , Bock, Hans Georg (Author) , Potschka, Andreas (Author)
Format: Article (Journal)
Language:English
Published: 23 April 2020
In: Automatica
Year: 2020, Volume: 117
ISSN:0005-1098
DOI:10.1016/j.automatica.2020.109001
Online Access:Verlag, lizenzpflichtig, Volltext: https://dx.doi.org/10.1016/j.automatica.2020.109001
Verlag, lizenzpflichtig, Volltext: http://www.sciencedirect.com/science/article/pii/S0005109820301990
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Author Notes:Jürgen Gutekunst, Hans Georg Bock, Andreas Potschka

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520 |a Feedback control for averaged infinite horizon problems is a challenging task because the optimal way to operate such systems often exhibits a time-varying behavior, i.e. it cannot be represented as a steady state. We present a controller that is based on the excellent approximation properties of periodic solutions to such systems. The controller is capable of autonomously adapting both the optimal periodic trajectory as well as the optimal period itself in case the system parameters change. The amount of necessary a priori information for the controller setup is reduced compared to other Economic Model Predictive Control (EMPC) schemes and the resulting economic performance of the closed-loop is superior to schemes that use a fixed period. Complementary to the standard stability-theory for EMPC, our approach does not require dissipativity conditions and is based solely on assumptions on controllability of the dynamical system, existence of optimal periodic trajectories with descent directions for suboptimal periodic orbits and regularity of the EMPC subproblems. Based on these assumptions we show that the resulting closed-loop economically performs equally well as the optimal periodic trajectory. We illustrate the results with a numerical simulation of a highly nonlinear, unstable air-borne powerkite under varying wind conditions. 
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