Optimal Control for Einstein Telescope

Current gravitational-wave (GW) detectors face fundamental sensitivity limits below 10 Hz, driven largely by low-frequency seismic noise. Achieving effective isolation across complex GW instruments is a challenging experimental and control problem due to multi-subsystem coupling, tilt-to-translation coupling, and nonlinear interactions between ground motion and active control loops. This thesis addresses these limitations by unifying optimal control design framework. To streamline optimization in high-dimensional systems, a novel multi-scale optimal control framework is introduced. The method employs a fundamental control-loop suppression limit—defined as an "acausal optimum" curve—to assess global optimality and simplify control synthesis. This approach is applied to candidate active seismic isolation platforms for the Einstein Telescope (ET), including OmniSens. OmniSens is a novel 6-degree-of-freedom active seismic isolation system utilizing a low-loss pendulum with interferometric sensors. This demonstrates the ability to optimize models with dozens of coupled state variables simultaneously. The commissioning of OmniSens is detailed through the characterization of its sensors, actuators, and electronics, experimentally validating the low-complexity mathematical models developed earlier for the platform. Systematic calibration, actuator tuning to minimize cross-couplings, and open-loop transfer function measurements demonstrate strong agreement between physical laboratory results and models. Finally, the thesis critically evaluates standard Linear Time-Invariant (LTI) and Gaussian assumptions by reframing seismic isolation as a prediction problem, paving the way for future non-LTI control techniques. Together, these theoretical frameworks, modeling tools, and experimental validations provide key technical building blocks to enable target low-frequency sensitivity in next-generation detectors like the Einstein Telescope.