Abstract
In this paper, we consider the chaos control for 4D hyperchaotic system by two cases, known & unknown parameters based on Lyapunov stability theory via nonlinear control. We find that there are two cofactors that have an effect on determining any case to achieve the control, the two cofactors are proposed in the control and the matrix that produce from the time derivative of Lyapunov function. In adding, we find some weakness cases in Lyapunov stability theory. For this reason, we design with only one controller and perform a simple change in this control in order to recognize the difference between these cases although all of the controllers are almost similar.
Highlights
Chaos phenomenon was firstly observed by Lorenz in 1963 [1]-[4]
When can we achieve chaos control with known parameters? Second, when can we achieve chaos control with unknown parameters? And third, how can we distinguish between these two cases? This paper begins with the suggestion of a new method that will answer these questions
We study the chaos control for 4D hyperchaotic system based on Lyapunov stability theory, where this method is effective and accurate in finding stability of systems, and in view of dealing with nonlinear parts of systems and not neglecting those parts which support the strength and accuracy
Summary
Chaos phenomenon was firstly observed by Lorenz in 1963 [1]-[4]. Chaos control is one of the chaos phenomena, which contains two aspects, namely, chaos control and chaos synchronization [5]. Some of the previous works achieved control and synchronization with unknown parameters only and. (2016) Control and Synchronization with Known and Unknown Parameters. F. Al-Azzawi another some achieved control and synchronization with known parameters only. We perform some simple change into this control, study probability of suppression for each control by using Lyapunov stability theory and get three cases. We can achieve control directly when parameters are unknown; in second type, we need to modify in order to achieve control with known parameters; in third type, it is imposable to perform the control. When can we achieve chaos control with known parameters? When can we achieve chaos control with unknown parameters? When can we achieve chaos control with known parameters? Second, when can we achieve chaos control with unknown parameters? And third, how can we distinguish between these two cases? This paper begins with the suggestion of a new method that will answer these questions
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