Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance

Abstract

This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

“…Like its integer-order version, [58] system (25) has only one equilibrium 𝐸 0 = {0, 0, 0, 0}. As it has been proved, [58] system (25) When the time-step h = 10 −3 , the coefficients γ = 0.1 and η i = 0.1, i = 1, 2, 3, 4, the numerical results are depicted in Figs. 1(a)-1(c).…”

“…[9] Intensive studies confirmed theoretically and physically that the chaotic and hyperchaotic behaviors exist the nonlinear fractional-order systems. [3,[8][9][10][11][12][13][14][15] Meanwhile, synchronization of fractional-order chaotic systems also has attracted increasing attention due to its potential applications in secure communication [16,17] and digital cryptography. [18][19][20] A variety of control schemes have been proposed to control and synchronize fractional-order chaos in infinite or finite time, [21,22] such as active control, [23,24] sliding mode control, [25][26][27] adaptive control, [28] passive control, [29] and impulsive control.…”

“…[3,[8][9][10][11][12][13][14][15] Meanwhile, synchronization of fractional-order chaotic systems also has attracted increasing attention due to its potential applications in secure communication [16,17] and digital cryptography. [18][19][20] A variety of control schemes have been proposed to control and synchronize fractional-order chaos in infinite or finite time, [21,22] such as active control, [23,24] sliding mode control, [25][26][27] adaptive control, [28] passive control, [29] and impulsive control. [30][31][32][33][34] Both fractional-order models and controllers have more degrees of freedom besides memory and hereditary effects.…”

H ∞ synchronization of the coronary artery system with input time-varying delay

“…To counter these nonlinear disturbances, lots of techniques have been proposed, such as adaptive tracking control, [15] model predictive control, [16,17] fuzzy control, [18][19][20][21] sliding mode control. [22][23][24][25][26] H ∞ control is a valid approach to reduce the effect caused by disturbances. As the application of H ∞ control, H ∞ synchronization for a chaotic system is studied in Ref.…”