2024/05/12 by Tobias Ritschel, Ritschel, Tobias K. S., John Wyller +1 · 1 citation
Computer Science · Engineering · #Advanced Algorithms and Applications #Blind Source Separation Techniques #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Neural Networks and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2405.07328
openalex publication_date 2024/05/12 · openalex created_date 2024/05/15 · openalex updated_date 2026/07/28
Time delays are ubiquitous in industry and nature, and they significantly affect both transient dynamics and stability properties. Consequently, it is often necessary to identify and account for the delays when, e.g., designing a model-based control strategy. However, identifying delays in differential equations is not straightforward and requires specialized methods. Therefore, we propose an algorithm for identifying distributed delays in delay differential equations (DDEs) that only involves simulation of ordinary differential equations (ODEs). Specifically, we 1) approximate the kernel in the DDEs (also called the memory function) by the probability density function of a mixed Erlang distribution and 2) use the linear chain trick (LCT) to transform the resulting DDEs into ODEs. Finally, the parameters in the kernel approximation are estimated as the solution to a dynamical least-squares problem, and we use a single-shooting approach to approximate this solution. We demonstrate the efficacy of the algorithm using numerical examples that involve the logistic equation and a point reactor kinetics model of a molten salt nuclear fission reactor.