On the square-root modification of the Gillijns—De Moor algorithm

The article considers a method for numerical identification of boundary conditions of the mathematical model of convection-diffusion-reaction based on the data of noisy measurements of the values of the desired function. To solve this problem, a transition is made from the initial continuous model with a partial differential equation to a discrete linear stochastic system in the state space, in which the functions included in the boundary conditions are represented as an unknown input vector. A square-root modification of the recurrent Gillijns—De Moor algorithm for simultaneous estimation of state and input vectors is applied to the resulting system. The results of a numerical experiment confirming the practical applicability of the proposed approach are presented.