Convergence analysis of run-to-run control for a class of nonlinear systems

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 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 of 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.