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Evolutionary Optimization Algorithms for Differential Equation Parameters, Initial Value and Order Identification

A dynamic system identification problem is considered. It is an inverse modelling problem, where one needs to find the model in an analytical form and a dynamic system is represented with the observation data. In this study the identification problem was reduced to an optimization problem, and in such a way every solution of the extremum problem determines a linear differential equation and coordinates of the initial value. The proposed approaches do not require any assumptions of the system order and the initial value coordinates and estimates the model in the form of a linear differential equation. These variables are estimated automatically and simultaneously with differential equation coefficients. Problem-oriented evolution-based optimization techniques were designed and applied. Techniques are based on the evolutionary strategies algorithm and have been improved to achieve efficient solving of the reduced problem for every proposed determination scheme. Experimental results confirm the reliability of the given approach and the usefulness of the reduced problem solving tool.