The Atlantic meridional overturning circulation (AMOC), an important component of the climate system, has only been directly measured since the RAPID array’s installation across the Atlantic at 26°N in 2004. This has shown that the AMOC strength is highly variable on monthly timescales; however, after an abrupt, short-lived, halving of the strength of the AMOC early in 2010, its mean has remained ~15% below its pre-2010 level. To attempt to understand the reasons for this variability, we use a control systems identification approach to model the AMOC, with the RAPID data of 2004–2017 providing a trial and test data set. After testing to find the environmental variables, and systems model, that allow us to best match the RAPID observations, we reconstruct AMOC variation back to 1980. Our reconstruction suggests that there is inter-decadal variability in the strength of the AMOC, with periods of both weaker flow than recently, and flow strengths similar to the late 2000s, since 1980. Recent signs of weakening may therefore not reflect the beginning of a sustained decline. It is also shown that there may be predictive power for AMOC variability of around 6 months, as ocean density contrasts between the source and sink regions for the North Atlantic Drift, with lags up to 6 months, are found to be important components of the systems model.