Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

Abstract

This article 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 the 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 linear quadratic regulator (LQR) control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. state perturbations. Both the 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 the robust nonlinear control theory to complex geosystems, earthquakes, and sustainable energy production.