Intelligent modeling of unknown distributed parameter systems

A spectral approximation based intelligent modeling approach is studied for some class of nonlinear parabolic PDE systems, for which the spatial operator is linear dominant, the main knowledge of actuator is known and the knowledge of sensor is accurately known. The eigenfunctions of the known linear part of spatial operat or are employed as a basis set of a Galerkin procedure to reduce the PDE system to a low-order ODE system with uncertain parameters and unknown nonlinearities. Then, a neural observer can be designed to estimate the states of the ODE model from the measurements of finite number sensors. Using the estimated states, a hybrid general regression neural network is trained to be a nonlinear model of the PDE system in state-space formulation, which is suitable for further applying traditional control techniques. Simulations on catalytic rod and real-time experiments on snap curing oven show that the modeling method is effective. © 2005 SICE.