A Multi-objective Approach with a Restart Meta-heuristic for the Linear Dynamical Systems Inverse Mathematical Problem

This study is focused on the automatic modelling of linear dynamical systems based on system output observations. Identification of a differential equation degree and its parameters requires the initial point because the output of the dynamical system for the given input depends on the initial point value. Generally, it is impossible to estimate the system state and its derivatives using the observation values, so the inverse mathematical modelling problem for dynamical systems can be reduced to a simultaneous approximation of the differential equation and the initial point. Solving the reduced two-criterion extremum problem requires a searching algorithm with specific problem-oriented modifications.