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

Abstract

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 kinds 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.

Preventing Instabilities and Inducing Controlled, Slow‐Slip in Frictionally Unstable Systems

“…Consequently, if the input respects Equation ( 17 ) or, equivalently, Equation ( 14 ), then or and so the reference input step command, , is tracked robustly. For time varying reference trajectories, , we expect a steady state error, which can be eliminated by adding more integrators (that is., double integrators, see Tzortzopoulos, 2021a ; Gutiérrez‐Oribio et al., 2022 ) or reduced by increasing the relevant integral action gains.…”