Chaos control for the Lorenz system

Abstract

This article presents an analysis of the chaotic dynamics presented by the Lorenz system and how this behavior can be eliminated through the implementation of sliding mode control. It is necessary to know about the theory of stability of Lyapunov to develop the appropriate control that allows to bring the system to the desired point of operation.

Study of the dynamics of a Lienard system

“…Indeed, the systemẍ + µ(x 2 − 1)ẋ + tanh(x) = 0 for µ > 0 has a stable limit cycle around the equilibrium solution (0, 0). To prove this, we see that the equation satisfies the conditions of the Liénard theorem [6]. Comparing Eqs.…”

Stability analysis of a magnetic levitator

“…We now want to linearize the system around the equilibrium points to know how stability is defined in these points. For this it is necessary first to obtain the Jacobian matrix of the system [7], as shown below. Therefore, using the Poincaré-Bendixon theorem we have the following.…”

Lorenz Kaotik Sisteminin Doğrusal Geri Beslemeli, Yüksek Kazanç, Yüksek Frekans ve Model Öngörülü Kontrol ile Kontrolü

“…Bu tasarımda kararsız Tasarım geri besleme kontrolörü sistemi kontrolsüz olan Lorenz sisteminin denge noktalarından birine taşınmasına yönelik bir çalışma gerçekleştirmişleridir [19]. Yeap [29]. Yau ve ark.…”