This paper highlights the relevance of evolving granular fuzzy systems in adaptive control and fuzzy modeling, particularly for learning in dynamic, nonstationary environments. These systems incrementally construct rule-based models—such as predictors and controllers operating in open- or closed-loop configurations—by adapting both structure and parameters from data streams. This provides a flexible and autonomous alternative to traditional parametric-adaptive approaches. We consolidate foundational concepts in fuzzy and adaptive control, positioning evolving systems as data-driven extensions of classical schemes. Key challenges are discussed, including safety-aware adaptation to drift, memory mechanisms, interpretability, and principled structural evolution. Building on these foundations, we develop a more mature formulation of the state-space evolving granular modeling and control framework (SS-EGM/SS-EGC), introducing a decay-rate–oriented treatment that advances the methodology beyond mere LMI feasibility toward online optimality. A compact case study on the chaotic Hénon map illustrates the approach: an online SS-EGM learned from data streams supports SS-EGC synthesis that stabilizes the map under bounded inputs. One-step prediction accuracy and decay-rate estimates confirm real-time viability. The framework provides a flexible basis that can be further extended in multiple directions to address the identified challenges.
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