Probabilistic fuzzy logic controller for uncertain nonlinear systems

This paper proposes a probabilistic fuzzy proportional - integral (PFPI) controller for controlling uncertain nonlinear systems. Firstly, the probabilistic fuzzy logic system (PFLS) improves the capability of the ordinary fuzzy logic system (FLS) to overcome various uncertainties in the controlled dynamical systems by integrating the probability method into the fuzzy logic system. Moreover, the input/output relationship for the proposed PFPI controller is derived. The resulting structure is equivalent to nonlinear PI controller and the equivalent gains for the proposed PFPI controller are a nonlinear function of input variables. These gains are changed as the input variables changed. The sufficient conditions for the proposed PFPI controller, which achieve the bounded-input bounded-output (BIBO) stability are obtained based on the small gain theorem. Finally, the obtained results indicate that the PFPI controller is able to reduce the effect of the system uncertainties compared with the fuzzy PI (FPI) controller.