Robust boundary tracking control of wave PDE: Insight on forcing slow-aseismic response

Abstract

The output boundary tracking problem is addressed for a wave partial differential equation (PDE) with uncertain multiplicative parameters and additive boundary and in-domain terms. To solve this problem, a homogeneous boundary feedback controller is designed using collocated boundary measurements only. Global exponential Input-to-State Stability (eISS) of the closed-loop system and its insensitivity to matched disturbances are additionally achieved. The ultimate bound estimate is diminished by tuning of the controller gains and/or by an appropriate pre-selection of a reference signal to follow. The proposed homogeneity-based strategy is further evaluated in a simplified earthquake model for controlled dissipation of its stored energy and producing slow-aseismic response. Such a case study possesses important applications in earthquake prevention, renewable energy production and storage. Numerical simulations are additionally conducted to support the robustness and the smoothness of the resulting closed-loop system depending on the homogeneous control parameter selection.