Towards Type-3 Fuzzy Control Stability with a Fuzzy Lyapunov Approach: The Case of a Robotic Manipulator

Stability is one of the relevant and key topics in Control. Type-3 Fuzzy Logic is a potential striking area for realizing fuzzy control. This article utilizes a Fuzzy Lyapunov approach, originally proposed for type-1 fuzzy control, to initially formulate a stable type-2 fuzzy controller. Then we propose an elevation from the Type-2 to Type-3, maintaining stability, with the fuzzy Lyapunov approach, of the corresponding fuzzy controller. The main contribution is to offer a first step on how to move forward with providing stability for type-3 fuzzy controllers. As a case study we consider a robotic manipulator to illustrate the proposal. The presented results demonstrate the potential of the type-3 fuzzy Lyapunov extension in the control area.