Fuzzy control for uncertainty nonlinear systems with dual fuzzy equations

Many uncertain nonlinear systems can be modeled by the linear-in-parameter model, and the parameters are uncertain in the sense of fuzzy numbers. Fuzzy equations can be used to model these nonlinear systems. The solutions of the fuzzy equations are the controllers. In this paper, we give the controllability condition for the fuzzy control via dual fuzzy equations. Two types of neural networks are applied to approximate the solutions of the fuzzy equations. These solutions are then transformed into the fuzzy controllers. The novel methods are validated with five benchmark examples.