Convergence Analysis of Run-to-run Control for a Class of Nonlinear Systems

Gregory Francois*, B. Srinivasan, D. Bonvin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In run-to-run control, measurements from previous runs are used to push the outputs of the current run towards desired set points. From a run-to-run perspective, the classical dynamics get integrated by each run, thereby leading to a static nonlinear input-output map. This paper shows that, when successive linearization of this nonlinear map is used to adapt the run-to-run controller, convergence may not be achieved. However, convergence can be guaranteed if the controller is based on a linear approximation for which the outputs are in-phase (i.e. within 90°) with the true outputs. A convergence proof based on Lyapunov approach is provided. The theoretical aspects are illustrated through the simulated meal-to-meal control of blood glucose concentration in diabetic patients.

Original languageEnglish
Pages (from-to)3032-3037
Number of pages6
JournalProceedings of the American Conference
Publication statusPublished - 2003


  • Blood glucose control
  • Convergence analysis
  • Diabetes management
  • Run-to-run control
  • Sector nonlinearity
  • Successive linearization


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