Fuzzy control of unstable chaotic systems

Abstract EN

This paper focuses on modeling 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 modeling phase, a Takagi–Surgeon (T–S) fuzzy system with Gaussian fuzzy membership functions is used in conjunction with the Liebenberg 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 modeling and control phases, some simulation results are provided on the logistic equation.