A supervisory controller for fuzzy control systems that guarantees stability

A supervisory controller is a controller which operates only when some undesirable phenomena occur, e.g., when the state hits the boundary of constraint set. In this note, the author develops a supervisory controller for a nonlinear fuzzy control systems. The supervisory controller works in the following way: if the fuzzy control system (without the supervisory controller) is stable in the sense that the state is inside the constraint set, the supervisory control is idle; if the state hits the boundary of the constraint set, the supervisory controller begins operation to force the state back to the constraint set. The author proves that the fuzzy control system equipped with this supervisory controller is globally stable in the sense that the state is guaranteed to be within the constraint set specified by the system designer. The author also proposes schemes by continuously switching between supervisory and nonsupervisory modes. Finally, the author applies a fuzzy controller with the supervisory controller to the inverted pendulum balancing problem where it is required that the state variables must be within a fixed bound