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Conference Papers Year : 2022

Advances in sliding mode control of earthquakes via boundary tracking of wave and diffusion PDEs

Abstract

Two recent results on earthquake control are summarized. A simplified model of an earthquake phenomenon is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the actuator dynamics as a diffusion process. In order to avoid a fast slip (earthquakelike behaviour), the control is designed to follow a slow reference. The control strategies are presented separately for both Partial Differential Equations (PDEs). For the wave PDE, a homogeneous boundary tracking control is developed to achieve exponential Input to State Stability (eISS) of the error closedloop dynamics. For the diffusion PDE, Proportional Integral (PI) and a discontinuous integral term are coupled to exponentially stabilize the error origin despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.
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Dates and versions

hal-03774399 , version 1 (10-09-2022)

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  • HAL Id : hal-03774399 , version 1

Cite

Diego Gutierrez-Oribio, Yury Orlov, Ioannis Stefanou, Franck Plestan. Advances in sliding mode control of earthquakes via boundary tracking of wave and diffusion PDEs. 16th International Workshop on Variable Structure Systems and Sliding Mode Control, Sep 2022, Rio de Janeiro, Brazil. ⟨hal-03774399⟩
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