A Set-Theoretic Method for Verifying Feasibility of a Fast Explicit Nonlinear Model Predictive Controller

  • Davide M. Raimondo
  • Stefano Riverso
  • Sean Summers
  • Colin N. Jones
  • John Lygeros
  • Manfred Morari
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 417)


In this chapter an algorithm for nonlinear explicit model predictive control is presented. A low complexity receding horizon control law is obtained by approximating the optimal control law using multiscale basis function approximation. Simultaneously, feasibility and stability of the approximate control law is ensured through the computation of a capture basin (region of attraction) for the closed-loop system. In a previous work, interval methods were used to construct the capture basin (feasible region), yet this approach suffered due to slow computation times and high grid complexity.

In this chapter, we suggest an alternative to interval analysis based on zonotopes. The suggested method significantly reduces the complexity of the combined function approximation and verification procedure through the use of DC (difference of convex) programming, and recursive splitting. The result is a multiscale function approximation method with improved computational efficiency for fast nonlinear explicit model predictive control with guaranteed stability and constraint satisfaction.


Model Predictive Control Outer Approximation Reachability Analysis Interval Extension Operator Bisect 
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 London 2012

Authors and Affiliations

  • Davide M. Raimondo
    • 1
  • Stefano Riverso
    • 2
  • Sean Summers
    • 1
  • Colin N. Jones
    • 1
  • John Lygeros
    • 1
  • Manfred Morari
    • 1
  1. 1.Automatic Control LaboratoryETHZürichSwitzerland
  2. 2.Dipartimento di Informatica e SistemisticaLaboratorio di Identificazione e Controllo dei Sistemi Dinamici, Universit‘a degli Studi di PaviaPaviaItaly

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