A Computational Framework to Control Verification and Robustness Analysis

This paper presents a methodology for evaluating the robustness of a controller based on its ability to satisfy the design requirements. The framework proposed is generic since it allows for high-fidelity models, arbitrary control structures and arbitrary functional dependencies between the requirements and the uncertain parameters. The cornerstone of this contribution is the ability to bound the region of the uncertain parameter space where the degradation in closed-loop performance remains acceptable. The size of this bounding set, whose geometry can be prescribed according to deterministic or probabilistic uncertainty models, is a measure of robustness. The robustness metrics proposed herein are the parametric safety margin, the reliability index, the failure probability and upper bounds to this probability. The performance observed at the control verification setting, where the assumptions and approximations used for control design may no longer hold, will fully determine the proposed control assessment.