Identification of a class of parabolic distributed parameter systems via deterministic learning

In this paper, we investigate identification of a class of distributed parameter systems (DPS) with both spatially invariant and spatially varying parameters via deterministic learning. The plant is a parabolic type partial differential equation (PDE) describing the propagation of heat conduction in a one-dimensional circle. We firstly employ the discrete Fourier transform (DFT) and the Inverse discrete Fourier transform (IDFT) techniques to transform the infinite-dimensional DPS into a finite-dimensional nonlinear dynamical system described by a set of ordinary differential equations (ODE). Secondly, we present an identifiability condition by placing certain requirements on the input function, which guarantees that the heat conduction process is persistently excited. The properties of finite-dimensional nonlinear system dynamics, including the discrete symmetry and the partial dominance of system dynamics according to point-wise observations are analyzed. Finally, by using the deterministic learning algorithm, locally accurate NN approximations of the finite-dimensional nonlinear systems are achieved in local region along the recurrent system trajectory. The identification is achieved not for the spatially invariant and spatially varying parameters, but instead for for the dynamics of the DPS. Thus, a new method for locally accurate identification of the parabolic DPS describing the propagation of heat conduction process is presented.