Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

Abstract

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

“…Consequently, impulsive control can save communication bandwidth and energy consumption. It has found extensive applications in time-varying delay systems [4], chaotic systems [5], and neural networks [6]. On the other hand, the event-triggered mechanism, as a control strategy that updates control information based on the system state, can effectively conserve communication resources, reduce energy consumption, and boasts high robustness and adaptability.…”

Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains

“…Recently, fractional-order nonlinear systems (FONSs), as the extension of integer-order nonlinear systems, have received considerable attention due to the attractive properties of fractional calculus in modeling and characterizing accurate dynamical properties of natural phenomena. To achieve the predefined control goals, numerous control methods have been presented to design controllers for FONSs, such as robust control [1,2], adaptive control [3,4], sliding mode control (SMC) [5,6], etc. In particular, the adaptive intelligent backstepping control technique has been widely used to handle the control problem of fractional-order nonlinear systems through integration with recursive control and an intelligent approximator [7][8][9].…”

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

“…The stabilization problem has already been extensively investigated for (hyper)chaotic financial systems; the interested readers can consult, for instance, References [13,14,[25][26][27], for some intuition and new observations concerning this topic. Analogously to the stabilization problem, the synchronization problem for (hyper)chaotic financial systems has also been investigated in several references; see References [28][29][30][31][32][33]. Synchronization is one of the most interesting collective behaviors of dynamical systems, and therefore has aroused tremendous interest in many application fields, such as secure communication, biological systems, and information processing; see References [26,[34][35][36][37] and the references cited therein.…”