Evolving granular fuzzy control: Overview, case study on the chaotic Hénon map, and research outlook

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.