This article deals with the estimation and control of a class of distributed parameter processes dominated by nonlinear diffusion. The major challenges in control of such systems lie in the nonlinear infinite-dimensional nature of the systems and the lack of direct sensing for relevant system states. In the proposed scheme, the proper orthogonal decomposition-Galerkin method is adopted to derive a reduced-order model in terms of temporal coefficients from the original system described by nonlinear partial differential equation(s). To overcome the sensing problem, the unscented Kalman filter is implemented to estimate the temporal coefficients of the reduced-order model online and subsequently reconstruct the distributed system states. A set of improved sufficient conditions are also established to ensure stability of the estimation scheme. Then, once these difficulties are addressed, a nonlinear model predictive control scheme is formulated to achieve desired control objectives such as trajectory tracking for distributed states, energy optimization and quality control. The proposed estimation and control scheme is demonstrated via an application to infrared drying of coatings in the automotive industry.
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