Fuzzy control of nonlinear systems using two standard techniques

The problem of the control of discrete-time nonlinear systems for which there is no available analytic model is tackled in this paper. Based on the ability of fuzzy systems to approximate any nonlinear mapping, the unknown nonlinear system is represented by a Takagi-Sugeno fuzzy model which is identified using input-output data. The control problem is then solved using a standard technique. Two different approaches are considered in this paper. The first one is a version of input-output linearization of discrete-time nonlinear systems. The advantage of this technique is the possibility to attenuate the influence of unstructured uncertainties on the control performances by introducing an additive control component. The second developed strategy is internal model control which is based on the introduction of an explicit fuzzy model of the plant in the control structure. Perfect control is obtained when the controller is chosen as the inverse of the fuzzy model. Finally, simulation results are included to demonstrate the feasibility of both proposed methods.