Set-membership estimation for weakly nonlinear models: an application to the adaptive control of semiconductor manufacturing processes

Considers an application of set-membership concepts to the parameter estimation problem for weakly nonlinear models. The authors develop a recursive algorithm that, given input-output data, a bound on the measurement noise and a local bound on the Hessian of the nonlinear model with respect to the unknown parameters, produces a consistent ellipsoid containing the “actual” model parameters. To illustrate the use of this algorithm, the authors consider the process of oxidation of silicon in dry oxygen where the oxidation time is determined by means of a simple adaptive controller. In an effort to reduce the parametric uncertainty, the authors employ an auxiliary set-membership estimator to update the set of parameter constraints on-line and, thus, avoid unnecessary drifts of the adaptive controller parameters