Fuzzy Control of Unstable Chaotic Systems

This paper focuses on modelling and controlling an unstable chaotic system defined by a set of input–output data. This approach works in two phases: a model of the system is determined, and then a control mechanism is activated to stabilize unstable fixed point and unstable periodic orbit embedded in the chaotic system. In the modelling phase, a Takagi–Sugeno (T–S) fuzzy system with Gaussian fuzzy membership functions is used in conjunction with the Levenberg– Marquardt algorithm for the model parameters optimization. In the controller design phase, based on the fuzzy model above, a prediction-based controller is achieved for the stabilization on a fixed point or unstable periodic orbit. To illustrate the effectiveness of the proposed method for both fuzzy modelling and control phases, some simulation results are provided on the logistic equation.