Tracking Control of a Class of Chaotic Systems

Abstract

This paper investigates the asymptotic tracking control problem of the chaotic system. Firstly, a reference system is presented, the output of which can asymptotically track a given command. Then, a both physically implementable and simple controller is designed, by which the given chaotic system synchronizes the reference system, and thus the output of such chaotic systems can asymptotically track the given command. It should be pointed out that the output of the given chaotic system can asymptotically track arbitrary desired periodic orbits. Finally, several illustrative examples are taken as example to show the validity and effectiveness of the obtained results.

Synchronization of a Class of Chaotic Systems with Both Uncertainty and Disturbance by the UDE-Based Control Method

“…Chaotic synchronization refers to the fact that the unstable motion controlled by the chaotic system tends to move in angular phase or amplitude with a similar rhythm through a certain coupling relationship and it has a wide range of applications in communications encryption, information science, chaotic generator design, and chemical reactions [3][4][5][6][7][8], etc. In recent years, scholars had proposed a variety of control methods to realize the synchronization between the same chaotic systems or the different chaotic systems with different initial conditions (refer to [9][10][11][12][13][14][15][16][17][18][19][20]). Among many control methods, the adaptive feedback control method [20] has a wide range of applications due to its simple design and easy implementation.…”

“…As far as we know, for chaotic synchronization, most of the existing control methods [9][10][11][12][13] only deal with the chaotic systems whose systems do not include model uncertainty and external disturbance and even if some methods can be used to cancel the uncertainty and disturbance, but the uncertainty and the disturbance are assumed bounded. As a matter of fact, uncertainty and the disturbance of such systems cannot be avoided and are often very large.…”

Prescribed Performance Synchronization Control of Chaotic Systems with Unknown Control Gain Signs

“…Chaotic synchronization control is widely used in engineering, communication, and other fields. For different chaotic systems, many scholars have proposed some synchronization control schemes [1][2][3][4][5][6][7][8][9][10], such as fuzzy control, sliding mode control, backstepping control, adaptive control, and robust control. For example, based on the Takagi-Sugeno fuzzy model, Kumar and Khan [4] designed the adaptive synchronization of chaotic systems by utilizing linear matrix inequality.…”

Copious Closed Forms of Solutions for the Fractional Nonlinear Longitudinal Strain Wave Equation in Microstructured Solids

“…ese definitions have been being employed to convert the fractional nonlinear partial differential equations to nonlinear integer-order ordinary differential equation and then the computational and numerical schemes can be applied to get various types of solutions for these models and the examples of these schemes [18][19][20][21][22][23][24][25][26][27][28][29][30].…”