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Processes 2019, 7(4), 185; https://doi.org/10.3390/pr7040185

Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation

1
Institute of Flight System Dynamics, Technical University of Munich, 85748 Garching bei München, Germany
2
Department of Eng. Cybernetics, Norwegian University of Science and Technology, 7034 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Current address: Boltzmannstrasse 15, 85748 Garching bei München, GER.
These authors contributed equally to this work.
Received: 19 February 2019 / Revised: 22 March 2019 / Accepted: 26 March 2019 / Published: 30 March 2019
(This article belongs to the Special Issue Optimization for Control, Observation and Safety)
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Abstract

This study develops a chance–constrained open–loop optimal control (CC–OC) framework capable of handling rare event probabilities. Therefore, the framework uses the generalized polynomial chaos (gPC) method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting chance constraint (CC) evaluation is based on the efficient sampling provided by the gPC expansion. The subset simulation (SubSim) method is used to estimate the actual probability of the rare event. Additionally, the discontinuous CC is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the SubSim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general CCs within an open–loop optimal control problem (OCP) at a low computational cost to calculate optimal results with rare failure probability CCs. View Full-Text
Keywords: robust open-loop optimal control; generalized polynomial chaos; chance constraints; subset simulation; open-loop optimal control; battery charge–discharge robust open-loop optimal control; generalized polynomial chaos; chance constraints; subset simulation; open-loop optimal control; battery charge–discharge
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Piprek, P.; Gros, S.; Holzapfel, F. Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation. Processes 2019, 7, 185.

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