Internal Nonlinear Predictive Control of Semilinear Parabolic Equations

This paper introduces a method for synthesizing reduced-order nonlinear model-based predictive controllers that have support in an arbitrary open subset, for semilinear parabolic equations. The predictive control law is computed based on reduced-order, nonlinear multi-step-ahead finiteelement predictors, identified directly from experimental input-output data. An advantage of this approach is that it does not require knowledge of the partial differential equation (PDE) model of the process. The proposed approach is computationally efficient and suitable for real-time implementation as it does not involve solving a complex nonlinear programming problem. The design method can deal effectively with load disturbances and noise in a similar manner to that adopted in the classical Generalized Predictive Control framework. The method is used to design and evaluate numerically a nonlinear predictive controller for a one-dimensional nonlinear parabolic equation.