Numerical Optimal Control of Nonlinear Systems

  • Lars Grüne
  • Jürgen Pannek
Part of the Communications and Control Engineering book series (CCE)


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.


Optimal Control Problem Equality Constraint Interior Point Method Merit Function Discretization Technique 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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