Fuzzy Control Systems: Past, Present and Future

TLDR

Since its introduction over 40 years ago, fuzzy logic control has evolved, with Mamdani fuzzy control initially model‑free and expert‑based, and growing interest in model‑based Takagi‑Sugeno and singleton‑type systems due to a lack of systematic frameworks. This paper reviews the key features of Mamdani, Takagi‑Sugeno, and singleton‑type fuzzy systems, highlighting their historical rationale and current research mainstreams. The review focuses on fuzzy model‑based approaches that employ Lyapunov stability theory and linear matrix inequality formulations. The authors conclude with a personal perspective on future directions and challenges in fuzzy control research.

Abstract

More than 40 years after fuzzy logic control appeared as an effective tool to deal with complex processes, the research on fuzzy control systems has constantly evolved. Mamdani fuzzy control was originally introduced as a model-free control approach based on expert?s experience and knowledge. Due to the lack of a systematic framework to study Mamdani fuzzy systems, we have witnessed growing interest in fuzzy model-based approaches with Takagi-Sugeno fuzzy systems and singleton-type fuzzy systems (also called piecewise multiaffine systems) over the past decades. This paper reviews the key features of the three above types of fuzzy systems. Through these features, we point out the historical rationale for each type of fuzzy systems and its current research mainstreams. However, the focus is put on fuzzy model-based approaches developed via Lyapunov stability theorem and linear matrix inequality (LMI) formulations. Finally, our personal viewpoint on the perspectives and challenges of the future fuzzy control research is discussed.