Skip to main content

Real-Time Sequential Convex Programming for Optimal Control Applications

  • Conference paper
  • First Online:
Modeling, Simulation and Optimization of Complex Processes

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. 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. 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. 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. 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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. T. Ohtsuka: A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica, 40(4):563–574, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. M. Robinson: Strongly regular generalized equations. Mathematics of Operations Research, 5(1):43-62, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  13. V. M. Zavala and L.T. Biegler: The Advanced Step NMPC Controller: Optimality, Stability and Robustness. Automatica, 45:86–93, 2009.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tran Dinh Quoc .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Quoc, T.D., Savorgnan, C., Diehl, M. (2012). Real-Time Sequential Convex Programming for Optimal Control Applications. In: Bock, H., Hoang, X., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25707-0_8

Download citation

Publish with us

Policies and ethics