Numerical Identification of Reaction-Diffusion Model Parameters under Unknown Boundary Conditions

The paper considers the problem of numerical identification of reaction-diffusion model parameters based on the results of measuring the values of the function of interest. The solution to the problem stated is based on the transition from the original continuous-time model to a discrete-time, linear stochastic model with unknown input signals, represented by difference equations in state space. The use of an instrumental identification criterion allows for the calculation of estimates for unknown model parameters. To calculate the values of the instrumental criterion in the identification algorithm, the Gillijns and De Moor algorithm for the recurrent simultaneous estimation of state vector and input signal is used. Simulation results demonstrate the workability of the proposed approach.