  This paper addresses the possibility of using robust control theory for
preventing earthquakes through fluid injections in the earth's crust. The
designed robust controllers drive aseismically a fault system to a new
equilibrium point of lower energy by tracking a slow reference signal. The
control design is based on a reduced-order nonlinear model able to reproduce
earthquake-like instabilities. Uncertainties related to the frictional and
mechanical properties of the underlying physical process and external
perturbations are considered. Two types of controllers are derived. The first
one is based on sliding-mode theory and leads to local finite-time convergence
of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The
second controller is based on LQR control and presents global exponential
stability of the tracking error and rejection of Lipschitz w.r.t. states
perturbations. Both controllers generate a continuous control signal,
attenuating the chattering effect in the case of the sliding-mode algorithms.
The developed controllers are tested extensively and compared on the basis of
numerical simulations and experiments in the laboratory. The present work opens
new perspectives for the application of robust nonlinear control theory to
complex geosystems, earthquakes and sustainable energy production.
