Real-Time Sequential Convex Programming for Optimal Control Applications

  • Tran Dinh Quoc
  • Carlo Savorgnan
  • Moritz Diehl
Conference paper


This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a byproduct, a new proof of the local convergence of sequential convex programming. The approach is illustrated by an example where RTSCP is applied to nonlinear model predictive control.


Model Predictive Control Sequential Quadratic Programming Interior Point Method Nonlinear Model Predictive Control Model Predictive Control Algorithm 
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  1. 1.
    L.T. Biegler: Efficient solution of dynamic optimization and NMPC problems. In: F. Allgöwer and A. Zheng (ed), Nonlinear Predictive Control, vol. 26 of Progress in Systems Theory, 219–244, Basel Boston Berlin, 2000.Google Scholar
  2. 2.
    L.T. Biegler and J.B Rawlings: Optimization approaches to nonlinear model predictive control. In: W.H. Ray and Y. Arkun (ed), Proc. 4th International Conference on Chemical Process Control - CPC IV, 543–571. AIChE, CACHE, 1991.Google Scholar
  3. 3.
    H.G. Bock, M. Diehl, D.B. Leineweber, and J.P. Schlöder: A direct multiple shooting method for real-time optimization of nonlinear DAE processes. In: F. Allgöwer and A. Zheng (ed), Nonlinear Predictive Control, vol. 26 of Progress in Systems Theory, 246–267, Basel Boston Berlin, 2000.Google Scholar
  4. 4.
    M. Diehl: Real-Time Optimization for Large Scale Nonlinear Processes. vol. 920 of Fortschr.-Ber. VDI Reihe 8, Meß-, Steuerungs- und Regelungstechnik, VDI Verlag, Düsseldorf, 2002.Google Scholar
  5. 5.
    M. Diehl, H.G. Bock, and J.P. Schlöder: A real-time iteration scheme for nonlinear optimization in optimal feedback control. SIAM J. on Control and Optimization, 43(5):1714–1736, 2005.zbMATHCrossRefGoogle Scholar
  6. 6.
    M. Diehl, H.G. Bock, J.P. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer: Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. J. Proc. Contr., 12(4):577–585, 2002.CrossRefGoogle Scholar
  7. 7.
    M. Diehl, R. Findeisen, and F. Allgöwer: A stabilizing real-time implementation of nonlinear model predictive control. In: L. Biegler, O. Ghattas, M. Heinkenschloss, D. Keyes, and B. van Bloemen Waanders (ed), Real-Time and Online PDE-Constrained Optimization, 23–52. SIAM, 2007.Google Scholar
  8. 8.
    M. Diehl, R. Findeisen, F. Allgöwer, H.G. Bock, and J.P. Schlöder: Nominal Stability of the Real-Time Iteration Scheme for Nonlinear Model Predictive Control. IEE Proc.-Control Theory Appl., 152(3):296–308, 2005.CrossRefGoogle Scholar
  9. 9.
    A. Helbig, O. Abel, and W. Marquardt: Model Predictive Control for On-line Optimization of Semi-batch Reactors. Pages 1695–1699, Philadelphia, 1998.Google Scholar
  10. 10.
    T. Ohtsuka: A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica, 40(4):563–574, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    S. M. Robinson: Strongly regular generalized equations. Mathematics of Operations Research, 5(1):43-62, 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    H. Seguchi and T. Ohtsuka: Nonlinear Receding Horizon Control of an Underactuated Hovercraft. International Journal of Robust and Nonlinear Control, 13(3–4):381–398, 2003.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    V. M. Zavala and L.T. Biegler: The Advanced Step NMPC Controller: Optimality, Stability and Robustness. Automatica, 45:86–93, 2009.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tran Dinh Quoc
    • 1
  • Carlo Savorgnan
    • 1
  • Moritz Diehl
    • 1
  1. 1.Department of Electrical Engineering (ESAT-SCD) and Optimization in Engineering Center (OPTEC)K.U. LeuvenLeuvenBelgium

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