A globally convergent run-to-run control algorithm with improved rate of convergence

Run-to-run control consists of using the measurements from previous runs to drive the outputs of the current run towards desired set points. From a run-to-run perspective, a dynamic system can be viewed as a static input-output map. For systems where this static map corresponds to a sector nonlinearity, a globally convergent fixed-gain run-to-run control algorithm has been recently proposed by the authors. This paper shows that it is possible to improve the rate of convergence of this algorithm by adapting its gain. Thus, the run-to-run controller switches from a Broyden update to a fixed low-gain update whenever it is necessary to jump over a local minimum. This algorithm is shown to be globally convergent for systems with sector nonlinearities.