کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
758997 | 896458 | 2012 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model](/preview/png/758997.png)
In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.
► We propose an MPC for a class of PDE systems with unknown nonlinearities.
► Galerkin method is used to derive a finite dimensional ODE.
► A Multilayer NN is employed to parameterize the unknown nonlinearities.
► A Galerkin/NN-based ODE model is used to predict future states in the MPC.
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 1, January 2012, Pages 388–404