# Sigmapoint Approach for Robust Optimization of Nonlinear Dynamic Systems

### Sebastian Recker, Peter Kühl, Moritz Diehl, Hans Georg Bock

#### Abstract

Mathematical models describing dynamic processes contain parametric uncertainties. Robust model-based optimization thus becomes a challenging task in process engineering. Current approaches either require high computational effort or they make use of oversimplified approximations that do not capture changes in the solution structure due to nonlinear effects of the uncertain parameters on the states of the process. In this paper we propose an improved optimization approach that uses sigmapoints to characterize the space of uncertain parameters. Propagating sigmapoints through the process model and directly using them in the optimization problem allows to capture relevant nonlinearities for the uncertain parameters. Main advantages of this simple yet elegant approach are the relatively low computational burden and the independence from the optimizer, as no further derivatives are needed. The approach is applied to two examples from process engineering, a batch distillation and a semibatch reactor.

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#### Paper Citation

#### in Harvard Style

Recker S., Kühl P., Diehl M. and Georg Bock H. (2012). **Sigmapoint Approach for Robust Optimization of Nonlinear Dynamic Systems** . In *Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8565-20-4, pages 199-207. DOI: 10.5220/0004026401990207

#### in Bibtex Style

@conference{simultech12,

author={Sebastian Recker and Peter Kühl and Moritz Diehl and Hans Georg Bock},

title={Sigmapoint Approach for Robust Optimization of Nonlinear Dynamic Systems},

booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2012},

pages={199-207},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004026401990207},

isbn={978-989-8565-20-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - Sigmapoint Approach for Robust Optimization of Nonlinear Dynamic Systems

SN - 978-989-8565-20-4

AU - Recker S.

AU - Kühl P.

AU - Diehl M.

AU - Georg Bock H.

PY - 2012

SP - 199

EP - 207

DO - 10.5220/0004026401990207