AIChE Journal, Vol.54, No.8, 2065-2081, 2008
Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process
A method is develol)edfior model 1,wedictive control of nonlinear stochastic partial Q ercntial equations (PDEs) to regulate the state variance, which phvsically rel)resents the roughticss ol'a sia.face in a thinfilin growth process, to a desired level. InitiallY a nonlinear stochastic PDE is.formidated into a system of in * finite nonlincal, stochastic ordinar d t rential equations bY itsing Galerkin's inethod. A finite-dimenSional al)proximaiion is then derived that cal)tures the donzinant mode contribi.ition to the state variance. A model In-edictivc control problent isfiOrmulated, based on the finite-dimensional aly)roximation, so that thefiiture state variance can be predicted in a computationally e0cient way. To demonstrate the method, the model predictive controller is al)plied to the stochastic 10tramoto-SivashinskY equation, and the kinetic Monte Carlo model of a s1nittering jw-ocess to regulate the sulf ce roughness at a desired level. (c) 2008 American Institute of Cheinical Engineers.