Comparison of six implicit real-time optimization schemes

Grégory François*, Bala Srinivasan, Dominique Bonvin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Real-time optimization (RTO) is a class of methods that use measurements to reject the effect of uncertainty on optimal performance. This article compares six implicit RTO schemes, that is, schemes that implement optimality not through numerical optimization but rather via the control of appropriate variables. For unconstrained processes, the ideal controlled variable is the cost gradient. It is shown that, because of their structural differences, model-free and model-based techniques exhibit different features in terms of required excitation, convergence, scalability with the number of inputs and rejection of uncertainty. This comparison is illustrated through a simulated CSTR.

Original languageEnglish
Pages (from-to)291-305
Number of pages15
JournalJournal Européen des Systèmes Automatisés
Issue number2-3
Publication statusPublished - 2012


  • Extremum-seeking control
  • Finite differences
  • Gradient estimation
  • Neighboring-extremal control
  • Real-time optimization
  • Self-optimizing control


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