Control and synchronization of a hyperchaotic system based on passive control

Abstract

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of the equilibrium point, a Poincaré map, the bifurcation diagram, and the Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.

A Fractional-Order Chaotic System with an Infinite Number of Equilibrium Points

“…Equation (17) indicates that the chaotic synchronization between fractional-order chaotic system (1) and fractionalorder chaotic system (8) can be achieved. The proof is completed.…”

“…However, for all the previous integer-order and fractional-order chaotic (hyperchaotic), many systems have a finite number of equilibrium points. For example, some chaotic systems have one equilibrium point [15][16][17], some chaotic systems have two equilibrium points [18], and some chaotic systems have three equilibrium points [1,2,5,6,9,10], so a natural and interesting question is can we construct a chaotic (hyperchaotic) system which has an infinite number of equilibrium points? Moreover, many fractionalorder chaotic and hyperchaotic systems also possess chaotic attractor for its corresponded integer-order system, so the other question is as follows: are the fractional-order chaotic and hyperchaotic systems no-chaotic behavior for its corresponded integer-order system?…”

Neural adaptive chaotic control with constrained input using state and output feedback

“…[7]. In the following decades, many advanced control methods were reported, such as impulsive control, [8][9][10] adaptive-dynamic-programmingbased optimal control, [11,12] ℋ ∞ synchronization, [13][14][15] passive control, [16,17] backstepping, [18,19] and so on. The methods mentioned above were developed based on the assumption that the control signals can be implemented by the serving actuator.…”

Finite-time sliding mode synchronization of chaotic systems

“…[10] Since Pecora and Carroll [11] proved that chaotic systems could be synchronized and realized a synchronization between chaotic circuits, a wide variety of control strategies have been proposed to synchronize different chaotic systems, such as active control, [12] backstepping control, [13] impulsive control, [14] intermittent control, [15] adaptive control, [16] H ∞ control, [17] projective synchronization, [18] linear matrix inequality techniques, [19] feedback control, [20] fuzzy logic control, [21] state observer control, [22] and passive control. [23] However, in many control schemes, the convergence time cannot be assigned in advance. In other words, the slave system cannot synchronize with the master system within a prespecified convergence time.…”