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

In this paper we consider an application of set-membership concepts to the parameter estimation problem for weakly nonlinear models. We 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, we 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, we 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.