Data-Driven Delay Identification with SINDy

In this work, we investigate the capabilities of the sparse identification of nonlinear dynamics method for time-delay identification. A possible solution is shown how delayed terms can be introduced into the method. We test the robustness and effectiveness of the method through data generated by simulation of different reference systems with known time delay. Through our test examples, we investigate the effect of noise and the delay distribution in the candidate terms. We also test the method in the presence of multiple delays. It is shown that by iterating through a range of threshold values with the STLSQ algorithm, the delayed terms can be identified in a robust manner.