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Approximated Constrained Optimal Control subject to Variable Parameters

IFAC-PapersOnLine 2020年第2期53卷 9310-9315页

作者： Christian Kallies Mohamed Ibrahim Rolf Findeisen Laboratory for Systems Theory and Automatic Control Otto von Guericke University Magdeburg Germany RF and CK are also affiliated to the International Max Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering Magdeburg Germany

Implementing optimal controllers on embedded systems can be challenging as it requires the solution of an optimization problem in real-time. Furthermore, the a priory verification of stability, e.g. not relying on the possibly numerical solution of an optimization problem is often not possible. We propose a non-linear control synthesis based on an approximated explicit solution of a constrained optimal control problem, which can be efficiently implemented and verified. The control law is derived based on a series expansion of an infinite horizon optimal control problem via Al’brekht‘s Method. In comparison to existing approaches we consider parametric uncertainties. The proposed method provides under certain conditions an approximated solution of the Hamilton–Jacobi–Bellman (HJB) equation. The feedback control law uses a finite number of terms of the series expansion, and therefore the evaluation does not require intensive online computation. Furthermore, the optimal control strategy does not only achieve an approximated infinite horizon performance but is also parameterized in terms of the varying parameters which are assumed to be known. We provide a proof of convergence and existence of the optimal control law. Simulation results with a non-linear quadcopter example show the effectiveness of the proposed strategy.

关键词： Approximated Infinite Horizon Optimal Control Al’brekht‘s Method Non-linear Infinite Horizon Adaptive Control Parametric Uncertainties

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Model Predictive Control of a Fed-batch Bioreactor Based on Dynamic Metabolic-Genetic Network Models

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IFAC-PapersOnLine 2018年第19期51卷 34-37页

作者： Jabarivelisdeh, Banafsheh Findeisen, Rolf Waldherr, Steffen for Advanced Methods in Process and System Engineering Magdeburg Germany Institute for Automation Engineering Center for Dynamical Systems Otto-von-Guericke-Universität Magdeburg Germany Department of Chemical Engineering KU Leuven Belgium Belgium

In this work, a model predictive control of a fed-batch bioreactor is presented, described by the dynamic enzyme-cost FBA model (deFBA). The deFBA model is employed within a bilevel optimization to obtain fed-batch operating policies including the substrate feeding and process-level regulation of metabolism for optimizing the productivity of a target product. The advantages of implementing the closed-loop control in order to compensate for modelling errors are evaluated by comparing with the performance of an open-loop control. A case study involving the fed-batch fermentation of Escherichia coli for ethanol production is considered to find optimal operating strategies for maximal productivity. © 2018

关键词： Model predictive control

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Robust Optimization of Dynamical systems with Correlated Random Variables using the Point Estimate Method

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IFAC-PapersOnLine 2018年第2期51卷 427-432页

作者： Xie, Xiangzhong Krewer, Ulrike Schenkendorf, René Institute of Energy and Process Systems Engineering Braunschweig University of Technology Braunschweig38106 Germany Braunschweig University of Technology Braunschweig38106 Germany for Advanced Methods in Process and Systems Engineering Magdeburg39106 Germany

Robust optimization of dynamical systems requires the proper uncertainty quantification. Monte Carlo simulations and polynomial chaos expansion are frequently used methods for uncertainty quantification and have been applied to a number of problems in process design and optimization. Both methods, however, are either computationally prohibitive for robust optimization or inappropriate for correlated random variables. The aim of this study is to introduce the point estimate method for optimization of dynamical systems with correlated random variables. The point estimate method requires only a few deterministic evaluations of the analyzed process model and estimates the statistical moments for robust optimization. The derived sample points can be adapted to random variables of arbitrary distributions and correlations. The contribution of this paper consists of presenting the point estimate method for correlated random variables in the field of model-based robust process design. The performance of the method is demonstrated with a case study of a continuous tubular reactor. © 2018

关键词： Uncertainty analysis Dynamical systems Estimation Intelligent systems Monte Carlo methods Optimization process design Random variables Arbitrary distribution Continuous tubular reactors Correlated model Design and optimization Point estimate method Polynomial chaos expansion Robust optimization Uncertainty quantifications

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Controller Parametrization for Offset-free Control Using Set-Based Feasibility methods

Controller Parametrization for Offset-free Control Using Set...

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American Control Conference

作者： Petar Andonov Anton Savchenko Rolf Findeisen IMPRS ProEng International Max Planck Research School Magdeburg for Advanced Methods in Process and Systems Engineering Germany Laboratory for Systems Theory and Automatic Control Otto-von-Guericke University Magdeburg Germany

ISBN: (纸本)9781538679012;9781538679265

Achieving a new set point and maintaining it with a desired precision is a common control problem. In case the reference is not fixed, or a priori unknown disturbances are present, the problem is often referred to as offset-free control. We consider the problem of finding suitable controller parameters to obtain an offset-free control up to a certain degree. We tackle the problem in two steps: first, we find controller parameters to steer the controlled system in the neighborhood of the desired reference;second, we identify controller parameters such that the system is robustly controlled invariant with respect to the desired neighborhood of the reference value. For each subproblem we determine the set of parameters that guarantee the desired behavior despite bounded uncertainties. We employ a set-based feasibility formulation which is able to handle nonlinear systems with set constraints. The approach is illustrated with an example.

关键词： Controllers reference value Free control Standing Orders parameterization parameters common control

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Theoretical and numerical analysis of the lattice kinetic scheme for complex-flow simulations

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Physical Review E 2019年第2期99卷 023305-023305页

作者： S. A. Hosseini N. Darabiha D. Thévenin Laboratory of Fluid Dynamics and Technical Flows University of Magdeburg “Otto von Guericke” D-39106 Magdeburg Germany Laboratoire EM2C CNRS CentraleSupélec Université Paris-Saclay 3 rue Joliot Curie 91192 Gif-sur-Yvette Cedex France International Max Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering Magdeburg 39106 Germany

The lattice kinetic scheme (LKS) is a modified version of the classical single relaxation time lattice Boltzmann method. Although used for many applications, especially when large variations in viscosity are involved, a thorough analysis of the scheme has not been provided yet. In the context of this work, the macroscopic behavior of this scheme is evaluated through the Chapman-Enskog analysis. It is shown that the additional degree of freedom provided in the scheme allows for an independent control of higher-order moments. These results are further corroborated by numerical simulations. The behavior of this numerical scheme is studied for selected external and internal flows to clarify the effect of the free parameter on the different moments of the distribution function. It is shown that it is more stable than SRT (single relaxation time) when confronted to fully periodic under-resolved simulations (especially for λ≈1). It can also help minimize the error coming from the viscosity-dependence of the wall position when combined with the bounce-back approach; although still present, viscosity-dependence of the wall position is reduced. Furthermore, as shown through the multiscale analysis, specific choices of the free parameter can cancel out the leading-order error. Overall, the LKS is shown to be a useful and efficient alternative to the SRT method for simulating numerically complex flows.

关键词： Cellular automata Complex fluids Flows in porous media Turbulence Lattice-Boltzmann methods Numerical techniques

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Extensive analysis of the lattice Boltzmann method on shifted stencils

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Physical Review E 2019年第6期100卷 063301-063301页

作者： S. A. Hosseini C. Coreixas N. Darabiha D. Thévenin Laboratory of Fluid Dynamics and Technical Flows University of Magdeburg “Otto von Guericke” D-39106 Magdeburg Germany Laboratoire EM2C CNRS CentraleSupélec Université Paris-Saclay 91192 Gif-sur-Yvette Cedex France International Max Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering Magdeburg Germany Department of Computer Science University of Geneva 1204 Geneva Switzerland

Standard lattice Boltzmann methods (LBMs) are based on a symmetric discretization of the phase space, which amounts to study the evolution of particle distribution functions (PDFs) in a reference frame at rest. This choice induces a number of limitations when the simulated flow speed gets closer to the sound speed, such as velocity-dependent transport coefficients. The latter issue is usually referred to as a Galilean invariance defect. To restore the Galilean invariance of LBMs, it was proposed to study the evolution of PDFs in a comoving reference frame by relying on asymmetric shifted lattices [N. Frapolli, S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 117, 010604 (2016)]. From the numerical viewpoint, this corresponds to overcoming the rather restrictive Courant-Friedrichs-Lewy conditions on standard LBMs and modeling compressible flows while keeping memory consumption and processing costs to a minimum (therefore using the standard first-neighbor stencils). In the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions (EDFs) and collision models. Thanks to them, it is possible to (1) better understand the effect of this solution on both physics and stability, (2) assess its viability as a way to extend the validity range of LBMs, and (3) quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path. The results clearly show that, in theory, the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity. Furthermore, just like the zero-Mach flow for the standard stencils, it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties. In addition, a detailed analysis of the obtained results shows that the properties of different collision models and EDFs remain unchanged under the shi

关键词： High-speed flow Lattice-Boltzmann methods

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Stability of the lattice kinetic scheme and choice of the free relaxation parameter

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Physical Review E 2019年第6期99卷 063305-063305页

作者： S. A. Hosseini C. Coreixas N. Darabiha D. Thévenin Laboratory of Fluid Dynamics and Technical Flows University of Magdeburg “Otto von Guericke” D-39106 Magdeburg Germany Laboratoire EM2C CNRS CentraleSupélec Université Paris-Saclay 3 rue Joliot Curie 91192 Gif-sur-Yvette Cedex France International Max Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering Magdeburg Germany Department of Computer Science University of Geneva Geneva Switzerland

The lattice kinetic scheme (LKS), a modified version of the classical single relaxation time (SRT) lattice Boltzmann method, was initially developed as a suitable numerical approach for non-Newtonian flow simulations and a way to reduce memory consumption of the original SRT approach. The better performances observed for non-Newtonian flows are mainly due to the additional degree of freedom allowing an independent control over the relaxation of higher-order moments, independently from the fluid viscosity. Although widely applied to fluid flow simulations, no theoretical analysis of LKS has been performed. The present work focuses on a systematic von Neumann analysis of the linearized collision operator. Thanks to this analysis, the effects of the modified collision operator on the stability domain and spectral behavior of the scheme are clarified. Results obtained in this study show that correct choices of the “second relaxation coefficient” lead, to a certain extent, to a more consistent dispersion and dissipation for large values of the first relaxation coefficient. Furthermore, appropriate values of this parameter can lead to a larger linear stability domain. At moderate and low values of viscosity, larger values of the free parameter are observed to increase dissipation of kinetic modes, while leaving the acoustic modes untouched and having a less pronounced effect on the convective mode. This increased dissipation leads in general to less pronounced sources of nonlinear instability, thus improving the stability of the LKS.

关键词： Lattice-Boltzmann methods

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Corrigendum to “Hybrid Lattice Boltzmann-Finite Difference model for low Mach number combustion simulation” [Combustion and Flame 209(2019) 394-404]

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Combustion and Flame 2020年 219卷 44-44页

作者： S.A. Hosseini H. Safari N. Darabiha D. Thévenin M. Krafczyk Laboratory of Fluid Dynamics and Technical Flows University of Magdeburg “Otto von Guericke” Magdeburg D-39106 Germany Laboratoire EM2C CNRS CentraleSupélec Université Paris-Saclay 3 rue Joliot Curie Gif-sur-Yvette Cedex 91192 France International Max Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering Magdeburg Germany Institute for Computational Modeling in Civil Engineering Technische Universität Braunschweig Germany

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Improving Bioprocess Productivity Using Constraint-Based Models in a Dynamic Optimization Scheme

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IFAC-PapersOnLine 2016年第26期49卷 245-251页

作者： Jabarivelisdeh, Banafsheh Waldherr, Steffen for Advanced Methods in Process and System Engineering Magdeburg Germany Institute for Automation Engineering Center for Dynamical Systems Otto-von-Guericke-Universität Magdeburg Germany Department of Chemical Engineering KU Leuven Belgium School of Engineering and Applied Sciences Harvard University United States

Modulating the expression of target genes is an effective metabolic engineering approach to increase bioprocess productivity. In this work, a bilevel optimization framework is applied for dynamic manipulation of gene expression based on constraint-based models. A dynamic model in the inner problem captures the network dynamics and enables temporal regulation of the metabolic network. Through linearization of nonlinear constraints, this framework is based on linear optimization which saves on computation time especially in a bilevel structure. A case study involving batch fermentation of Escherichia coli for ethanol production is considered to find an optimal manipulation strategy of metabolic networks for maximal productivity. © 2016

关键词： Metabolic engineering Escherichia coli Gene expression Linear programming Metabolism Productivity Bi level optimization Constraint based method Constraint based models Dynamic optimization Flux balance analysis Manipulation strategy Metabolic engineering approach Non linear constraints

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Stability preserving model reduction for linearly coupled linear time-invariant systems

Stability preserving model reduction for linearly coupled li...

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Joint 87th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2016 and Deutsche Mathematiker‐Vereinigung, DMV 2016

作者： Benner, Peter Grundel, Sara Mlinarić, Petar Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany for Advanced Methods in Process and System Engineering Magdeburg Germany

We develop a stability preserving model reduction method for linearly coupled linear time-invariant (LTI) systems. The method extends the work of Monshizadeh et al. for multi-agent systems with identical LTI agents. They propose using Bounded Real Balanced Truncation to preserve a sufficient condition for stability of the coupled system. Here, we extend this idea to arbitrary linearly coupled LTI systems using the sufficient condition for stability introduced by Reis and Stykel. The model reduction error bounds for this method also follow from results of Reis and Stykel, which allows the adaptive choice of reduced orders. We demonstrate the method on Reis’s and Stykel’s coupled string-beam example. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Linear time-invariant system

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