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Total solar irradiance variations, about 0.1% between solar activity maximumand minimum, are available from accurate satellite measurements since 1978 andthus do not provide useful information on longer-term secular trends. Recently,Krivova et al., 2007 reconstructed, using suitable models, the total solarirradiance from the end of the Maunder minimum to the present, based onvariations of the surface distribution of the solar magnetic field. The latteris calculated from the long historical record of the sunspot numbers using asimple but consistent physical model. There are many classes of proposedprediction methods for solar cycles behavior, based on different direct solaractivity indices or on various valuable proxies. In particular, the precursorbased methods, utilize a given proxy index to predict the future evolution ofsolar activity. Long-term time series of sunspot numbers, allow us to reliablypredict the behavior of the next solar cycle, few years in advance. In previouspapers we predicted the full-shape curve of future solar cycles, using a propernon-linear dynamics method applied to monthly smoothed sunspot numbers. Inparticular, we proved that a sufficiently reliable phase-amplitude predictionof the current solar cycle 24, requires the knowledge of the initial increasingphase of the cycle spanning at least two years. The aim of the present paper isto give a robust long-term prediction of solar cycle activity, many years inadvance and for at least three successive solar cycles using the same nonlinearmethod and, as solar activity proxy index, the reconstructed total solarirrandiance.

Reconstructed Total Solar Irradiance as a precursor for long-term solar activity predictions: a nonlinear dynamics approach