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Nonlinear Model Predictive Control pp 275–339Cite as

Numerical Optimal Control of Nonlinear Systems

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Part of the book series: Communications and Control Engineering ((CCE))

Abstract

In this chapter, we present methods for the numerical solution of the constrained finite horizon nonlinear optimal control problems which occurs in each iterate of the NMPC procedure. To this end, we first discuss standard discretization techniques to obtain a nonlinear optimization problem in standard form. Utilizing this form, we outline basic versions of the two most common solution methods for such problems, that is Sequential Quadratic Programming (SQP) and Interior Point Methods (IPM). Furthermore, we investigate interactions between the differential equation solver, the discretization technique and the optimization method and present several NMPC specific details concerning the warm start of the optimization routine. Finally, we discuss NMPC variants relying on inexact solutions of the finite horizon optimal control problem.

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Notes

  1. 1.

    Appropriate step lengthsα k will be added to these updates, below.

  2. 2.

    http://www.sbsi-sol-optimize.com/asp/sol_product_snopt.htm.

  3. 3.

    http://www.ai7.uni-bayreuth.de/nlpqlp.htm.

  4. 4.

    http://hqp.sourceforge.net.

  5. 5.

    http://www.coin-or.org/ipopt.

  6. 6.

    http://orfe.princeton.edu/loqo.

  7. 7.

    http://www.ziena.com.

  8. 8.

    http://www.worhp.de.

  9. 9.

    http://www.ist.uni-stuttgart.de/research/projects/ControlTheory/#mpc,http://www.nmpc.de.

  10. 10.

    http://www.acadotoolkit.org.

  11. 11.

    http://www.iwr.uni-heidelberg.de/groups/agbock/RESEARCH/muscod.php.

  12. 12.

    http://www.nonlinearmpc.com.

  13. 13.

    http://www.mathworks.com/products/mpc.

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  1. Mathematisches Institut, Universität Bayreuth, Bayreuth, 95440, Germany

    Jürgen Pannek

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  1. Lars Grüne
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Grüne, L., Pannek, J. (2011). Numerical Optimal Control of Nonlinear Systems. In: Nonlinear Model Predictive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-501-9_10

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  • DOI: https://doi.org/10.1007/978-0-85729-501-9_10

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