Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process
2008
A method is developed for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level. Initially a nonlinear stochastic PDE is formulated into a system of infinite nonlinear stochastic ordinary differential equations by using Galerkin's method. A finite-dimensional approximation is then derived that captures the dominant mode contribution to the state variance. A model predictive control problem is formulated, based on the finite-dimensional approximation, so that the future state variance can be predicted in a computationally efficient way. To demonstrate the method, the model predictive controller is applied to the stochastic Kuramoto-Sivashinsky equation, and the kinetic Monte Carlo model of a sputtering process to regulate the surface roughness at a desired level. © 2008 American Institute of Chemical Engineers AIChE J, 2008
Keywords:
- Stochastic partial differential equation
- Ordinary differential equation
- Stochastic differential equation
- Differential equation
- Mathematical optimization
- Model predictive control
- Continuous-time stochastic process
- Partial differential equation
- Nonlinear system
- Control theory
- Mathematics
- Applied mathematics
- Inorganic chemistry
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