A probabilistic approach to run-to-run control

This paper considers model uncertainty in the run-to-run control problem from a probabilistic viewpoint. The methodology assumes that the model parameters are stochastic and uses experimental input-output data off-line to characterize the probability distribution of the model parameters. This naturally leads to the notions of probability of stability and probability of performance as a means of evaluating run-to-run controllers. Analytic formulas for the probability of stability are given for the particular case of an EWMA controller. When considering a more general notion of performance, the Monte Carlo method is used to approximate the probability of performance to a high degree of confidence. This probabilistic approach to run-to-run control is then illustrated on a virtual plasma etching reactor. Finally, the reliability of the method is investigated.