Cognitive control is increasingly adopted in industrial automation due to its ability to learn, adapt, and optimize decisions online; however, its practical deployment is often limited by insufficient guarantees of stability and poor generalization under changing operating conditions. This paper investigates cognitive control algorithms from a unified perspective that links algorithmic stability (sensitivity to data perturbations) with generalization ability (performance retention under distribution and regime shifts) while maintaining closed-loop performance. A generic nonlinear discrete-time plant model is considered, and a cognitive control architecture is formulated with state estimation, decision-making policy, and online parameter updating. An experimental protocol is developed in a digital-twin environment using repeated trials across a structured set of scenarios, including nominal operation, parameter drift, increased disturbances, measurement noise, network delay/dropouts, regime switching, and distribution shift. Control quality is evaluated via integral error indices (IAE/ISE/ITAE) and control-effort measures, while learning robustness is quantified using an empirical algorithmic-stability indicator and a generalization gap . The results demonstrate a consistent trade-off between aggressive adaptation (improved nominal tracking) and increased sensitivity to data and condition shifts, highlighting that low is strongly associated with improved generalization under regime changes. The proposed methodology provides a reproducible framework for selecting and tuning cognitive controllers under explicit stability–generalization constraints, supporting safer and more reliable deployment in cyber-physical industrial systems.