# Restart Operator for Optimization Heuristics in Solving Linear Dynamical System Parameter Identification Problem

### Ivan Ryzhikov, Christina Brester

#### Abstract

In this study, the parameter identification problem for linear dynamical systems is considered. The system is assumed to be represented as a linear differential equation in general form, so the right-hand side equation contains input function and its derivatives. This problem statement extends the order reduction problem, where we need to find the equation of the lower order to approximate the real system output observations. Considered problem is reduced to an optimization one. The reduced problem is complex, and we propose the combination of stochastic optimization algorithm and restart operator. This operator aim is to prevent the algorithm stagnation by starting the search over again if no remarkable solution improvement is detected or if algorithm searches in the area where stagnation had been detected.

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