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Handling state constraints and economics in feedback control of transport-reaction processes

Liangfeng Lao, Matthew Ellis, Panagiotis D. Christofides
2015 Journal of Process Control  
In this work, we focus on systems of nonlinear parabolic PDEs and propose a novel EMPC design integrating adaptive proper orthogonal decomposition (APOD) method with a high-order finite-difference method  ...  The computational efficiency and constraint handling properties of this design are evaluated using a tubular reactor example modeled by two nonlinear parabolic PDEs.  ...  Acknowledgments Financial support from the National Science Foundation and the Department of Energy is gratefully acknowledged.  ... 
doi:10.1016/j.jprocont.2015.04.009 fatcat:f2ntojyqkjgsjcrysbman247iq

Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition: Application to hydraulic fracturing

Harwinder Singh Sidhu, Abhinav Narasingam, Prashanth Siddhamshetty, Joseph Sang-Il Kwon
2018 Computers and Chemical Engineering  
This study aims to overcome this challenge by introducing sparse proper orthogonal decomposition (SPOD)-Galerkin methodology.  ...  Developing reduced-order models for nonlinear parabolic partial differential equation (PDE) systems with time-varying spatial domains remains a key challenge as the dominant spatial patterns of the system  ...  *Reprinted with permission from "Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition: Application to hydraulic fracturing" by Sidhu  ... 
doi:10.1016/j.compchemeng.2018.02.004 fatcat:mnuf5rt2njg3nhe5iaxkrt4q6u

Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems

Weiguo Xie, Ioannis Bonis, Constantinos Theodoropoulos
2015 Journal of Process Control  
The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions.  ...  Model Predictive Control (MPC) has been effectively applied in process industries since the 1990s.  ...  Acknowledgements The authors would like to acknowledge the financial support of the EC FP6 Project:  ... 
doi:10.1016/j.jprocont.2015.07.009 fatcat:ixwywpxy3bbybdr5xzuu6cb7ay

On Aronsson Equation and Deterministic Optimal Control

Pierpaolo Soravia
2008 Applied Mathematics and Optimization  
The model is a nonlinear system of three differential equations with five controls.  ...  In this paper a general approach to the design of controllers for Nonlinear Control systems is presented.  ...  In order to enable real time control of the system model reduction techniques are needed. We choose the snapshot form of proper orthogonal decomposition (POD).  ... 
doi:10.1007/s00245-008-9048-7 fatcat:kihxqtczfzdn5pbmvsd42axbk4

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
., +, TAC Jan. 2020 143-158 Proper Orthogonal Decomposition Method to Nonlinear Filtering Problems in Medium-High Dimension.  ...  ., +, TAC Nov. 2020 4832- 4839 Proper Orthogonal Decomposition Method to Nonlinear Filtering Problems in Medium-High Dimension.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

2018 Index IEEE Transactions on Automatic Control Vol. 63

2018 IEEE Transactions on Automatic Control  
., +, TAC Jan. 2018 196-202 Model Reference Adaptive Control of 2 × 2 Coupled Linear Hyperbolic PDEs.  ...  ., +, TAC Nov. 2018 3881-3888 Model Reference Adaptive Control of 2 × 2 Coupled Linear Hyperbolic PDEs.  ... 
doi:10.1109/tac.2019.2896796 fatcat:bwmqasulnzbwhin5hv4547ypfe

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Peter Benner, Serkan Gugercin, Karen Willcox
2015 SIAM Review  
This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing  ...  Model reduction of linear, non-parametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books.  ...  Proper orthogonal decomposition.  ... 
doi:10.1137/130932715 fatcat:lfylrclfjvcxfo7wvxwx6lylb4

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Sebastian Peitz, Michael Dellnitz
2018 Mathematical and Computational Applications  
In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition.  ...  This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be  ...  Acknowledgments: This work is supported by the Priority Programme SPP 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems" of the German Research Foundation (DFG).  ... 
doi:10.3390/mca23020030 fatcat:zixdhh4uhvbufcxbbnmyf4uxji

Metamodeling techniques for CPU-intensive simulation-based design optimization: a survey

Hanane Khatouri, Tariq Benamara, Piotr Breitkopf, Jean Demange
2022 Advanced Modeling and Simulation in Engineering Sciences  
Thus, the concept of multi-fidelity proposes to merge different levels of fidelity within a single model with controlled variance.  ...  AbstractIn design optimization of complex systems, the surrogate model approach relying on progressively enriched Design of Experiments (DOE) avoids efficiency problems encountered when embedding simulation  ...  Acknowledgements The authors would like to thank Cenaero and Safran Aircraft Engines for their support and permission to publish this study, as well as Cenaero and the university of Technology of Compiegne  ... 
doi:10.1186/s40323-022-00214-y fatcat:4n7uucw445b5vcalrrxcrcwctq

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The resulting linear systems are solved alternatively by the Multigrid method and Krylov subspace methods. We treat two types of boundary conditions: Dirichlet and natural boundary condition.  ...  The solution is obtained by means of Finite Element Method (FEM).  ...  This problem can be formulated as an optimal control problem with state constraints, where the control can be the quantity of phytoplankton added at each tank or the permanence times, the state variables  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Certifying Unstability of Switched Systems Using Sum of Squares Programming

Benoît Legat, Pablo Parrilo, Raphaël Jungers
2020 SIAM Journal of Control and Optimization  
From an analysis and controller design point of view, it is known that GSPT and its adaptation to control systems [4], provide mathematical tools to understand the dynamics, and design controllers from  ...  Acknowledgements We argue that, from a modeling point of view, the assumptions of distinct timescales is ubiquitous when modeling complex systems.  ...  In a traditional periodic control setting, the delays are handled by selecting a sampling period either to accomodate the worst-case delay or according to the time constraints of the system and if the  ... 
doi:10.1137/18m1173460 fatcat:ytlzbwk7vbampbuyo6snenz33m

Table of contents

2009 2009 17th Mediterranean Conference on Control and Automation  
Adapted fuzzy controlled is suggested here in order to handle the control loops of a DCS system.  ...  This paper deals with sufficient conditions of asymptotic stability for non linear discrete-time 2D systems represented by a Takagi-Sugenofuzzy model of Roesser type with state feedback control.  ...  A large dynamic model of the nonlinear heat equation is obtained through finite element (FE), which is reduced using proper orthogonal decomposition.  ... 
doi:10.1109/med.2009.5164498 fatcat:bi37lbkbhfaihj7lbc64vvplo4

Methods in Oil Recovery Processes and Reservoir Simulation

Pablo Druetta, Pietro Tesi, Claudio De Persis, Francesco Picchioni
2016 Advances in Chemical Engineering and Science  
The aim of this review is to address the topics described. Firstly, the origin of an oil recovery process, the economic factors and field tests involved are introduced.  ...  As the computational power increased, more advanced and detailed models were developed, including different chemical and physical phenomena.  ...  the performance prediction of compositional models [72] .  ... 
doi:10.4236/aces.2016.64039 fatcat:icyyu3v72ne7fksttq6qdea7ne

Recent developments in model-based optimization and control of subsurface flow in oil reservoirs

Paul M.J. Van den Hof, Jan Dirk Jansen, Arnold Heemink
2012 IFAC Proceedings Volumes  
The past ten years have seen an increasing application of systems and control theory to porous media flow.  ...  In this paper we describe some recent contributions of our group to the use of systems and control theory for CLRM.  ...  ACKNOWLEDGMENTS The authors acknowledge the important contributions of many of their coworkers, including Gijs van Essen, Jorn Van Doren, Sippe Douma, Ali Vakili Ghahani, Malgorzata Kaleta, Mariya Krymskaya  ... 
doi:10.3182/20120531-2-no-4020.00047 fatcat:5n5q2ysrmvbg5gxbf6l3a7s4kq

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
The lack of the convergence is compensated for, first of all, by the flexibility in the choice of the basis functions and by the simplicity of the generalization to the multidimensional case.  ...  We present new a-posteriori error estimates for the indicated classes of problems and show that the corresponding adaptive algorithms for quantitative error control are reliable and efficient.  ...  systems arising from discretisations of symmetric elliptic PDEs.  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa
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