Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations

The Cauchy problem (also called the initial value problem) for the system of ordinary differential equations with right-hand sides depending on some unknown parameters is considered here. The noisy measurements of one of the variables at the given time moments are assumed to be known. A new algorithm for recovering (identification) the model parameters is proposed. The algorithm is based on the numerical integration of the gradient equations of some least-square functional. The right-hand sides of the gradient equations are obtained by the numerical integration of the Cauchy problem for the original equations and equations for their partial derivatives with respect to unknown parameters. Parameter identification for the well-known Lotka-Volterra model of oscillating chemical reaction demonstrates the robustness of the proposed algorithm when the measurements are corrupted with random multiplicative noise.