Nonlinear Model Predictive Control

  • Alexandra Grancharova
  • Tor Arne Johansen
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 429)


A nonlinear model predictive control (NMPC) strategy requires the formulation of an optimization problem. For online NMPC the nonlinear programming problem must be solved numerically at every sampling interval, while explicit NMPC assumes that an explicit representation of the solution can be computed using multi-parametric nonlinear programming. This chapter considers the formulation of the optimization problem, which is an essential part of the control design and involves numerous decisions that are important for the control performance, stability, and robustness as well as the computational complexity and the numerical challenges of computing the solution. Key elements are discretization and parameterization procedures that leads to a finite-dimensional numerical optimal control problem that can be addressed using e.g. direct single shooting, direct multiple shooting, or collocation methods. Fundamental properties like feasibility and continuity of solutions are discussed, before various modifications that are needed to explicitly guarantee stability, feasibility, and robustness, are discussed. We then discuss further extensions for handling integer variables, output feedback, decentralized and distributed implementations, before some remarks on numerical and computational challenges are discussed at the end.


Optimal Control Problem Model Predictive Control Sampling Instant Binary Search Tree Linear Parameter Vary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of System Engineering and RoboticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Engineering CyberneticsNorwegian University of Science and TechnologyTrondheimNorway

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