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Efficient Solution of Dynamic Optimization and NMPC Problems

  • Conference paper
Nonlinear Model Predictive Control

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 26))

Abstract

Large scale optimization strategies have evolved considerably over the past two decades. Currently, continuous variable optimization problems (nonlinear programs) are solved on-line for steady state refinery models with several hundred thousand variables. Moreover, efficient NLP strategies have been developed for dynamic optimization problems. Still, to take the next step, on-line optimization of large dynamic chemical processes, a number of limitations and research challenges must be overcome.

Many of the advances in NLP algorithms have taken place by recognizing and exploiting the framework of Successive Quadratic Programming (SQP) algorithms. These are extensions of Newton type methods for converging to the solution of the KKT (optimality) conditions of the optimization problem. Because of this, fast convergence can be expected and a number of standard devices can be added to stabilize the algorithm to converge from poor starting points. Limitations of these Newton-based methods are also well-known. They experience difficulties in the presence of ill conditioning and extreme nonlinearities. Also, for optimization algorithms, nonconvexity can also lead to a number of difficulties and there is a need for software that allows exploitable structures for specific problem classes.

A number of innovations in algorithm design and problem formulation address these issues and greatly improve performance. As a result, very fast NLP algorithms can be derived for data reconciliation, parameter estimation, nonlinear model predictive control and dynamic optimization. Moreover, inequality constraints and variable bounds can be treated through advances in interior point strategies. These methods preserve the particular problem structure and scale well in performance for large-scale problems with many constraints.

Finally, the ability to solve nonlinear programs quickly also allows us to consider more challenging problems. These include the extension to solving nonconvex NLPs globally and the ability to assess the solution’s tolerance to uncertainty by considering features of nonlinear programming sensitivity analysis and robust optimization through flexibility analysis and design.

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA-15213

    Lorenz T. Biegler

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  1. Lorenz T. Biegler
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Editors and Affiliations

  1. Institut für Systemtheorie technischer Prozesse, Universität Stuttgart, Pfaffenwaldring 9, Stuttgart, 70550, Germany

    Frank Allgöwer

  2. Department of Chemical Engineering, University of Massachusetts at Amherst, 159 Goessmann Lab, Amherst, 01003-3110, MA, USA

    Alex Zheng

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Biegler, L.T. (2000). Efficient Solution of Dynamic Optimization and NMPC Problems. In: Allgöwer, F., Zheng, A. (eds) Nonlinear Model Predictive Control. Progress in Systems and Control Theory, vol 26. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8407-5_13

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  • DOI: https://doi.org/10.1007/978-3-0348-8407-5_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9554-5

  • Online ISBN: 978-3-0348-8407-5

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