Adaptive NN-Based Reference-Tracking Control of Uncertain Nonlinear Parabolic PDE Systems

Abstract

This paper is focused on the reference-tracking control problem of distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with uncertain nonlinear dynamics. An adaptive tracking control scheme is developed by utilizing radial basis function neural networks (RBF NNs) to deal with nonlinear system uncertainties. Specifically, the Galerkin method is first employed to derive a reduced-order ordinary differential equation (ODE) model to approximate the original PDE system. Based on this, an adaptive tracking control scheme is developed based on the singular perturbation theory and Lyapunov stability theory. With the control scheme implemented on the original PDE system, the system output can be guaranteed to track a prescribed reference trajectory with desired system stability and tracking accuracy. Simulation study on a representative transport-reaction process is conducted to demonstrate the effectiveness of the proposed approach.