Adaptive Fuzzy Control for Uncertain Fractional-Order Financial Chaotic Systems Subjected to Input Saturation

Abstract

In this paper, control of uncertain fractional-order financial chaotic system with input saturation and external disturbance is investigated. The unknown part of the input saturation as well as the system’s unknown nonlinear function is approximated by a fuzzy logic system. To handle the fuzzy approximation error and the estimation error of the unknown upper bound of the external disturbance, fractional-order adaptation laws are constructed. Based on fractional Lyapunov stability theorem, an adaptive fuzzy controller is designed, and the asymptotical stability can be guaranteed. Finally, simulation studies are given to indicate the effectiveness of the proposed method.

Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters

“…See the Appendix A . It was pointed out [ 33 , 34 , 35 ] that a similar theorem is obtained for the real systems.…”

LMI Based Synchronization Control of Nonlinear Affine Fractional Order Chaotic Systems Considering Input Constraint

“…The presence of input saturation usually decreases the control performance of system or can cause oscillations and even lead to instability of the closed loop system [19]. Therefore, synchronization of chaotic systems considering input saturation, have received much attention from researchers [20][21][22]. However, it should be noted that this focus has been more on integer-order chaotic systems than fractionalorder ones.…”

LMI Based Synchronization Control of Nonlinear Affine Fractional Order Chaotic Systems Considering Input Constraint

“…For example, in [23] a memory-less nonlinear function is employed to handle the input saturation problem and a linear controller is designed to control the fractional order financial chaotic system. In [20], an adaptive fuzzy controller is designed for fractional order financial chaotic systems with inputs saturation in three dimension state space. In [21] an adaptive fuzzy synchronization controller is designed to synchronize two fractional order chaotic systems with input saturation and external disturbance.…”