Two fuzzy control schemes for Lorenz-Stenflo chaotic system

Abstract

In this paper, two effective fuzzy control schemes, i.e., fuzzy feedback control method and adaptive fuzzy control method are introduced to suppress the state variables of the Lorenz-Stenflo chaotic system (LSCS) to its equilibrium point. For the first fuzzy control scheme, with the abundant modeling capability of the T-S fuzzy model, the LSCS can be decomposed into some local linear systems, which makes it very convenient to use the fuzzy feedback control method to analyze it. Based on the Lyapunov stability theorem, a criterion is also derived to guarantee the controlled LSCS is robust stable at the equilibrium point, even if there exist external perturbations. For the second fuzzy control scheme, fuzzy logic systems areexploited to approximate the nonlinear functions. Moreover, an adaptive technique is employed to construct an effective fuzzy controller, which can drive all state variables into a rather small neighborhood of its equilibrium point. By choosing a group of suitable parameters, the controlled system can approach the equilibrium point with high precision. Two numerical simulations are presented to demonstrate the effectiveness and feasibility of the two fuzzy control schemes.