Nonlinear control applied to chaotic system using sliding mode

Abstract

In this paper, a nonlinear control strategy for chaotic system via sliding mode design is considered. Sliding Mode Control (SMC) is adequate for controlling chaotic system, since it offers robustness in the presence of parameter uncertainty and disturbances. It is guaranteed that, under the proposed control law, chaotic systems can asymptotically drive the system orbits to arbitrarily desired trajectories. The simulations of Chua circuit and Genesio tensi are presented to show the effectiveness of the method presented in the paper.

Chaos Synchronization Using Super-Twisting Sliding Mode Control Applied on Chua’s Circuit

“…The chattering phenomena can be eliminated by using the second order sliding mode control. However, Different second order sliding mode topology such as: the super twisting algorithm, drift algorithm, sub-optimal algorithm, and prescribed convergence algorithm are discussed in literature [16], [32]- [34]. Therefore, The Super-twisting algorithm is a second order sliding mode controller is more suitable for the system with relative degree one.…”

“…Chaos has been extensively investigated since Lorenz reported a sensitive dependence on initial conditions in an atmosphere prediction model and includes infinite unstable periodic motion. Therefore, attarcte the attention of research comuunity in all the branches dealing with evolutionary processes: chemistry, biology, medicine, genetics, economics, sociology and electronic systems [1][2][3][4][5][6][7]. One of the most popular nonlinear electronic systems is Chua's circuit which is a classical example of bifurcation and chaos in nonlinear circuits in many studies.…”

“…On the other side, random motion of a system in a chaotic situation was considered to be unfavorable in engineering fields. Therefore, many efforts were given to eliminate or control chaos in the systems, which led to launching the work on chaos control in 1990 such as the OGY (Ott, Gerbogi and York) control method [8], linear feedback control [9], [10], time delay feedback control [4], [11], [12] and some others were reported: the control of chaos such as sliding mode control [13][14][15][16], fuzzy control [17][18][19][20], polynomial approach [21] high order sliding mode control [22] and harmonic approach [23], [24], etc.…”